Theorem anabsi5 495

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 389	. 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 496  anabsi8 498  rcla4e 1868  hbsbc1gd 1979  hbsbcgd 1980  hbcsb1gd 2023  hbcsbgd 2024  onint 3001  onminex 3015  f1oweALT 3897  php2 4500  genpprecl 5084  prlem934 5119  pre-axsup 5271  projlem25 9149  gelsupvalOLD 10354

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