Theorem pm3.37 286

Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112.

Assertion

Ref	Expression
pm3.37	|- (((ph /\ ps) -> ch) -> ((ph /\ -. ch) -> -. ps))

Proof of Theorem pm3.37

Step	Hyp	Ref	Expression
1		pm3.21 284	. . . . 5 |- (ps -> (ph -> (ph /\ ps)))
2	1	imim1d 28	. . . 4 |- (ps -> (((ph /\ ps) -> ch) -> (ph -> ch)))
3	2	com12 11	. . 3 |- (((ph /\ ps) -> ch) -> (ps -> (ph -> ch)))
4		iman 237	. . 3 |- ((ph -> ch) <-> -. (ph /\ -. ch))
5	3, 4	syl6ib 212	. 2 |- (((ph /\ ps) -> ch) -> (ps -> -. (ph /\ -. ch)))
6	5	con2d 91	1 |- (((ph /\ ps) -> ch) -> ((ph /\ -. ch) -> -. ps))

Syntax hints:  -. wn 2   -> wi 3   /\ wa 223

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

This theorem depends on definitions:  df-bi 147  df-an 225

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