Theorem con2 106

Description: Contraposition. Theorem *2.03 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
con2	|- ((ph -> -. ps) -> (ps -> -. ph))

Proof of Theorem con2

Step	Hyp	Ref	Expression
1		notnot2 100	. . 3 |- (-. -. ph -> ph)
2	1	imim1i 19	. 2 |- ((ph -> -. ps) -> (-. -. ph -> -. ps))
3	2	con4d 91	1 |- ((ph -> -. ps) -> (ps -> -. ph))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  con2d 107  con2i 113  con2b 182  pm5.18 722  pm5.18OLD 723  mt2bi 781  ax4 1318  rankr1 5785

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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