Theorem con1 92

Description: Contraposition. Theorem *2.15 of [WhiteheadRussell] p. 102.

Assertion

Ref	Expression
con1	|- ((-. ph -> ps) -> (-. ps -> ph))

Proof of Theorem con1

Step	Hyp	Ref	Expression
1		negb 86	. . 3 |- (ps -> -. -. ps)
2	1	imim2i 17	. 2 |- ((-. ph -> ps) -> (-. ph -> -. -. ps))
3	2	a3d 75	1 |- ((-. ph -> ps) -> (-. ps -> ph))

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  con1d 93  pm2.37OLD 99  pm2.61 124  bi2.15 166  jao 340  nneob 4239  uzwo4OLD 6158  uzwo 6387  uzwoOLD 6388

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

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