Theorem simp1l 1005

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp1l	|- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ph )

Proof of Theorem simp1l

Step	Hyp	Ref	Expression
1		simpl 108	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	3ad2ant1 1002	1 |- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 964

This theorem is referenced by:  simpl1l  1032  simpr1l  1038  simp11l  1092  simp21l  1098  simp31l  1104  en2lp  4469  tfisi  4501  funprg  5173  nnsucsssuc  6388  ecopovtrn  6526  ecopovtrng  6529  addassnqg  7190  distrnqg  7195  ltsonq  7206  ltanqg  7208  ltmnqg  7209  distrnq0  7267  addassnq0  7270  mulasssrg  7566  distrsrg  7567  lttrsr  7570  ltsosr  7572  ltasrg  7578  mulextsr1lem  7588  mulextsr1  7589  axmulass  7681  axdistr  7682  dmdcanap  8482  lt2msq1  8643  ltdiv2  8645  lediv2  8649  xaddass  9652  xaddass2  9653  xlt2add  9663  modqdi  10165  expaddzaplem  10336  expaddzap  10337  expmulzap  10339  resqrtcl  10801  bdtrilem  11010  bdtri  11011  xrbdtri  11045  prmexpb  11829  cnptoprest  12408  ssblps  12594  ssbl  12595