Theorem simp-5l 549

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

Assertion

Ref	Expression
simp-5l	|- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ph )

Proof of Theorem simp-5l

Step	Hyp	Ref	Expression
1		simp-4l 547	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )
2	1	adantr 276	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ph )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  simp-6l  551  aptap  8980  xaddf  10256  nn0ltexp2  11161  xrmaxiflemlub  12030  dfgcd2  12807  ctiunctlemfo  13379  mhmmnd  13968  neitx  15418  limccnp2cntop  15827  limccoap  15828  lgsval  16221