Theorem simp-7r 813

Description: Simplification of a conjunction. (Contributed by Mario Carneiro, 4-Jan-2017.)

Assertion

Ref	Expression
simp-7r	|- ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )

Proof of Theorem simp-7r

Step	Hyp	Ref	Expression
1		simp-6r 811	. 2 |- ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) -> ps )
2	1	adantr 481	1 |- ( ( ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) /\ ze ) /\ si ) -> ps )

Syntax hints:   -> wi 4   /\ 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-an 386

This theorem is referenced by:  simp-8r  815  catass  16347  tgbtwnconn1  25470  legso  25494  miriso  25565  footex  25613  opphl  25646  lnopp2hpgb  25655  f1otrg  25751  2sqmo  29649  afsval  30749  smfmullem3  41000