Theorem simp3r2 1170

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp3r2	|- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )

Proof of Theorem simp3r2

Step	Hyp	Ref	Expression
1		simpr2 1068	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	3ad2ant3 1084	1 |- ( ( ta /\ et /\ ( th /\ ( ph /\ ps /\ ch ) ) ) -> ps )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  nllyrest  21289  cdlemblem  35079  cdleme21  35625  cdleme22b  35629  cdleme40m  35755  cdlemg34  36000  cdlemk5u  36149  cdlemk6u  36150  cdlemk21N  36161  cdlemk20  36162  cdlemk26b-3  36193  cdlemk26-3  36194  cdlemk28-3  36196  cdlemky  36214  cdlemk11t  36234  cdlemkyyN  36250  stoweidlem56  40273