Material conditional
History

In Arithmetices Principia: Nova Methodo Exposita (1889), Peano expressed the proposition "If A {\displaystyle A}, then B {\displaystyle B} " as A {\displaystyle A} Ɔ B {\displaystyle B} with the symbol Ɔ, which is the opposite of C. He also expressed the proposition A ⊃ B {\displaystyle A\supset B} as A {\displaystyle A} Ɔ B {\displaystyle B}. Hilbert expressed the proposition "If A, then B " as A → B {\displaystyle A\to B} in 1918. Russell followed Peano in his Principia Mathematica (1910–1913), in which he expressed the proposition "If A, then B " as A ⊃ B {\displaystyle A\supset B}. Following Russell, Gentzen expressed the proposition "If A, then B " as A ⊃ B {\displaystyle A\supset B}. Heyting expressed the proposition "If A, then B " as A ⊃ B {\displaystyle A\supset B} at first but later came to express it as A → B {\displaystyle A\to B} with a right-pointing arrow. Bourbaki expressed the proposition "If A, then B " as A ⇒ B {\displaystyle A\Rightarrow B} in 1954.
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