Theorem anabsi7 497

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabsi7.1	|- (ps -> ((ph /\ ps) -> ch))

Assertion

Ref	Expression
anabsi7	|- ((ph /\ ps) -> ch)

Proof of Theorem anabsi7

Step	Hyp	Ref	Expression
1		anabsi7.1	. . . 4 |- (ps -> ((ph /\ ps) -> ch))
2	1	exp3a 375	. . 3 |- (ps -> (ph -> (ps -> ch)))
3	2	pm2.43b 67	. 2 |- (ph -> (ps -> ch))
4	3	imp 350	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anabss7 503  elunii 2508  ordelord 2970  vtoclibr 3213  opelxpi 3217  fneu 3592  fvelrn 3812  sdomtr 4474  prnmax 5099

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

Copyright terms: Public domain