Theorem simp132 1142

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

Assertion

Ref	Expression
simp132	|- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ps )

Proof of Theorem simp132

Step	Hyp	Ref	Expression
1		simp32 1043	. 2 |- ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) -> ps )
2	1	3ad2ant1 1027	1 |- ( ( ( th /\ ta /\ ( ph /\ ps /\ ch ) ) /\ et /\ ze ) -> ps )

Syntax hints:   -> wi 4   /\ w3a 983

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 189  df-an 373  df-3an 985

This theorem is referenced by:  ax5seglem3  24953  3atlem1  32973  3atlem2  32974  3atlem5  32977  2llnjaN  33056  4atlem11b  33098  4atlem12b  33101  lplncvrlvol2  33105  dalemtea  33120  dath2  33227  cdlemblem  33283  dalawlem1  33361  lhpexle3lem  33501  4atexlemex6  33564  cdleme22f2  33839  cdleme22g  33840  cdlemg7aN  34117  cdlemg34  34204  cdlemj1  34313  cdlemk23-3  34394  cdlemk25-3  34396  cdlemk26b-3  34397