Theorem pm5.71 977

Description: Theorem *5.71 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 23-Jun-2005.)

Assertion

Ref	Expression
pm5.71	|- ( ( ps -> -. ch ) -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )

Proof of Theorem pm5.71

Step	Hyp	Ref	Expression
1		orel2 398	. . . 4 |- ( -. ps -> ( ( ph \/ ps ) -> ph ) )
2		orc 400	. . . 4 |- ( ph -> ( ph \/ ps ) )
3	1, 2	impbid1 215	. . 3 |- ( -. ps -> ( ( ph \/ ps ) <-> ph ) )
4	3	anbi1d 741	. 2 |- ( -. ps -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )
5		pm2.21 120	. . 3 |- ( -. ch -> ( ch -> ( ( ph \/ ps ) <-> ph ) ) )
6	5	pm5.32rd 672	. 2 |- ( -. ch -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )
7	4, 6	ja 173	1 |- ( ( ps -> -. ch ) -> ( ( ( ph \/ ps ) /\ ch ) <-> ( ph /\ ch ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386

This theorem is referenced by: (None)