Theorem simpr11 1078

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

Assertion

Ref	Expression
simpr11	|- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Proof of Theorem simpr11

Step	Hyp	Ref	Expression
1		simp11 1024	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ph )
2	1	adantl 464	1 |- ( ( et /\ ( ( ph /\ ps /\ ch ) /\ th /\ ta ) ) -> ph )

Syntax hints:   -> wi 4   /\ wa 367   /\ w3a 971

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 185  df-an 369  df-3an 973

This theorem is referenced by:  el2spthonot0  25017  cgr3tr4  29895  btwnoutside  29968  paddasslem8  36003  cdleme27a  36545