Theorem anabsi5 497

Description: Absorption of antecedent into conjunction.

Hypothesis

Ref	Expression
anabsi5.1	|- (ph -> ((ph /\ ps) -> ch))

Assertion

Ref	Expression
anabsi5	|- ((ph /\ ps) -> ch)

Proof of Theorem anabsi5

Step	Hyp	Ref	Expression
1		anabsi5.1	. . 3 |- (ph -> ((ph /\ ps) -> ch))
2	1	adantr 391	. 2 |- ((ph /\ ps) -> ((ph /\ ps) -> ch))
3	2	pm2.43i 64	1 |- ((ph /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  anabsi6 498  anabsi8 500  rcla4e 1875  hbsbc1gd 1986  hbsbcgd 1987  hbcsb1gd 2030  hbcsbgd 2031  onint 3012  onminex 3026  f1oweALT 3912  php2 4520  genpprecl 5116  prlem934 5151  pre-axsup 5303  projlem25 9205

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