Theorem simp-5r 534

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 532	. 2 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ps )
2	1	adantr 274	1 |- ( ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) /\ et ) -> ps )

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-6r  536  exmidfodomrlemr  7158  exmidfodomrlemrALT  7159  xaddf  9780  mulcncf  13231  suplociccreex  13242  cnplimclemr  13278