Theorem ex-natded5.7-2 27269

Description: A more efficient proof of Theorem 5.7 of [Clemente] p. 19. Compare with ex-natded5.7 27268. (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
ex-natded5.7.1	|- ( ph -> ( ps \/ ( ch /\ th ) ) )

Assertion

Ref	Expression
ex-natded5.7-2	|- ( ph -> ( ps \/ ch ) )

Proof of Theorem ex-natded5.7-2

Step	Hyp	Ref	Expression
1		ex-natded5.7.1	. 2 |- ( ph -> ( ps \/ ( ch /\ th ) ) )
2		simpl 473	. . 3 |- ( ( ch /\ th ) -> ch )
3	2	orim2i 540	. 2 |- ( ( ps \/ ( ch /\ th ) ) -> ( ps \/ ch ) )
4	1, 3	syl 17	1 |- ( ph -> ( ps \/ ch ) )

Syntax hints:   -> wi 4   \/ 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)