Theorem simp112 1191

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

Assertion

Ref	Expression
simp112	|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ps )

Proof of Theorem simp112

Step	Hyp	Ref	Expression
1		simp12 1092	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ps )
2	1	3ad2ant1 1082	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ps )

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:  axcontlem4  25847  ps-2b  34768  llncvrlpln2  34843  4atlem11b  34894  4atlem12b  34897  2lnat  35070  cdlemblem  35079  4atexlemex6  35360  cdleme24  35640  cdleme26ee  35648  cdlemg2idN  35884  cdlemg31c  35987  cdlemk26-3  36194  dihglblem2N  36583  0ellimcdiv  39881