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("!- \p. (snd p, fst p) : A*B -> B*A"
"->I"
("p : A*B !- (snd p, fst p) : B*A"
"*I"
("p : A*B !- snd p : B"
"*E2"
("p : A*B !- p : A*B"
"hyp"))
("p : A*B !- fst p : A"
"*E1"
("p : A*B !- p : A*B"
"hyp")))
@BekaValentine

BekaValentine commented Aug 29, 2016

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!- \p. (snd p, fst p) : A*B -> B*A     by ->I

    p : A*B !- (snd p, fst p) : B*A     by *I

        p : A*B !- snd p : B     by *E2

            p : A*B !- p : A*B     by hyp

        p : A*B !- fst p : A     by *E1

            p : A*B !- p : A*B    by hyp

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