Theorem simp121 1120

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

Assertion

Ref	Expression
simp121	|- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ph )

Proof of Theorem simp121

Step	Hyp	Ref	Expression
1		simp21 1021	. 2 |- ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) -> ph )
2	1	3ad2ant1 1009	1 |- ( ( ( th /\ ( ph /\ ps /\ ch ) /\ ta ) /\ et /\ ze ) -> ph )

Syntax hints:   -> wi 4   /\ w3a 965

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 371  df-3an 967

This theorem is referenced by:  ax5seglem3  23314  axpasch  23324  exatleN  33356  ps-2b  33434  3atlem1  33435  3atlem2  33436  3atlem4  33438  3atlem5  33439  3atlem6  33440  2llnjaN  33518  4atlem12b  33563  2lplnja  33571  dalempea  33578  dath2  33689  lneq2at  33730  llnexchb2  33821  dalawlem1  33823  osumcllem7N  33914  lhpexle3lem  33963  cdleme26ee  34312  cdlemg34  34664  cdlemg36  34666  cdlemj1  34773  cdlemj2  34774  cdlemk23-3  34854  cdlemk25-3  34856  cdlemk26b-3  34857  cdlemk26-3  34858  cdlemk27-3  34859  cdleml3N  34930