Theorem simp-5l 538

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 536	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )
2	1	adantr 274	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  simp-6l  540  xaddf  9801  nn0ltexp2  10644  xrmaxiflemlub  11211  dfgcd2  11969  ctiunctlemfo  12394  neitx  13062  limccnp2cntop  13440  limccoap  13441  lgsval  13699