Theorem simp-5r 550

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

Assertion

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

Proof of Theorem simp-5r

Step	Hyp	Ref	Expression
1		simp-4r 548	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ps )
2	1	adantr 276	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

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-6r  552  exmidfodomrlemr  7554  exmidfodomrlemrALT  7555  aptap  8978  xaddf  10246  mhmmnd  13919  mulcncf  15709  suplociccreex  15725  cnplimclemr  15770  usgr1vr  16489