Theorem simp231 1205

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

Assertion

Ref	Expression
simp231	|- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ph )

Proof of Theorem simp231

Step	Hyp	Ref	Expression
1		simp31 1097	. 2 |- ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) -> ph )
2	1	3ad2ant2 1083	1 |- ( ( et /\ ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ ze ) -> ph )

Syntax hints:   -> wi 4   /\ 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:  cdlemd4  35488  cdleme21ct  35617  cdleme21e  35619  cdleme21f  35620  cdleme21i  35623  cdleme26eALTN  35649  cdlemk23-3  36190  cdlemk25-3  36192