Theorem simp-5l 533

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 531	. 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  535  xaddf  9780  nn0ltexp2  10623  xrmaxiflemlub  11189  dfgcd2  11947  ctiunctlemfo  12372  neitx  12918  limccnp2cntop  13296  limccoap  13297  lgsval  13555