Editing Material conditional (section)

== History ==
In ''[[Arithmetices principia, nova methodo exposita|Arithmetices Principia: Nova Methodo Exposita]]'' (1889), [[Giuseppe Peano|Peano]] expressed the proposition "If <math>A</math>, then <math>B</math>" as <math>A</math> Ɔ <math>B</math> with the symbol Ɔ, which is the opposite of C.{{sfn|Van Heijenoort|1967}} He also expressed the proposition <math>A\supset B</math> as <math>A</math> Ɔ <math>B</math>.<ref>Note that the horseshoe symbol Ɔ has been flipped to become a subset symbol ⊂.</ref>{{sfn|Nahas|2022|page=VI}}{{sfn|Allegranza|2015}} [[David Hilbert|Hilbert]] expressed the proposition "If ''A'', then ''B''" as <math>A\to B</math> in 1918.{{sfn|Hilbert|1918}} [[Bertrand Russell|Russell]] followed Peano in his ''[[Principia Mathematica]]'' (1910–1913), in which he expressed the proposition "If ''A'', then ''B''" as <math>A\supset B</math>. Following Russell, [[Gerhard Gentzen|Gentzen]] expressed the proposition "If ''A'', then ''B''" as <math>A\supset B</math>. [[Arend Heyting|Heyting]] expressed the proposition "If ''A'', then ''B''" as <math>A\supset B</math> at first but later came to express it as <math>A\to B</math> with a right-pointing arrow.<!-- check https://jeff560.tripod.com/set.html later --> [[Nicolas Bourbaki|Bourbaki]] expressed the proposition "If ''A'', then ''B''" as <math>A \to B</math> in 1954.{{sfn|Bourbaki|1954|page=14}}