Theorem simp-5r 544

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 542	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ps )
2	1	adantr 276	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

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-6r  546  exmidfodomrlemr  7201  exmidfodomrlemrALT  7202  aptap  8607  xaddf  9844  mhmmnd  12980  mulcncf  14094  suplociccreex  14105  cnplimclemr  14141