Theorem simp2r 1008

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

Assertion

Ref	Expression
simp2r	|- ( ( ph /\ ( ps /\ ch ) /\ th ) -> ch )

Proof of Theorem simp2r

Step	Hyp	Ref	Expression
1		simpr 109	. 2 |- ( ( ps /\ ch ) -> ch )
2	1	3ad2ant2 1003	1 |- ( ( ph /\ ( ps /\ ch ) /\ th ) -> ch )

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:  simpl2r  1035  simpr2r  1041  simp12r  1095  simp22r  1101  simp32r  1107  issod  4241  funprg  5173  fsnunf  5620  f1oiso2  5728  tfrlemibxssdm  6224  ecopovtrn  6526  ecopovtrng  6529  addassnqg  7190  ltsonq  7206  ltanqg  7208  ltmnqg  7209  addassnq0  7270  recexprlem1ssl  7441  mulasssrg  7566  distrsrg  7567  lttrsr  7570  ltsosr  7572  ltasrg  7578  mulextsr1lem  7588  mulextsr1  7589  axmulass  7681  axdistr  7682  dmdcanap  8482  lediv2  8649  ltdiv23  8650  lediv23  8651  xaddass2  9653  xlt2add  9663  expaddzaplem  10336  expaddzap  10337  expmulzap  10339  expdivap  10344  leisorel  10580  bdtrilem  11010  xrbdtri  11045  fldivndvdslt  11632  prmexpb  11829  cnptoprest  12408  ssblps  12594  ssbl  12595  tgqioo  12716