Theorem simp-4r 508

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

Assertion

Ref	Expression
simp-4r	|- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ps )

Proof of Theorem simp-4r

Step	Hyp	Ref	Expression
1		simpllr 500	. 2 |- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ps )
2	1	adantr 270	1 |- ( ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  simp-5r  510  supinfneg  8683  infsupneg  8684