Theorem simp-5l 543

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 541	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ph )
2	1	adantr 276	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ph )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  simp-6l  545  aptap  8609  xaddf  9846  nn0ltexp2  10691  xrmaxiflemlub  11258  dfgcd2  12017  ctiunctlemfo  12442  mhmmnd  12985  neitx  13853  limccnp2cntop  14231  limccoap  14232  lgsval  14490