Theorem simp113 1192

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

Assertion

Ref	Expression
simp113	|- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ch )

Proof of Theorem simp113

Step	Hyp	Ref	Expression
1		simp13 1093	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) -> ch )
2	1	3ad2ant1 1082	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th /\ ta ) /\ et /\ ze ) -> ch )

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  llncvrlpln2  34843  4atlem12b  34897  2lnat  35070  cdlemblem  35079  4atexlemex6  35360  cdleme24  35640  cdleme26ee  35648  cdlemg2idN  35884  dihglblem2N  36583  0ellimcdiv  39881  limclner  39883