Theorem simp1l 1011

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 1008	1 |- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ph )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

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 970

This theorem is referenced by:  simpl1l  1038  simpr1l  1044  simp11l  1098  simp21l  1104  simp31l  1110  en2lp  4531  tfisi  4564  funprg  5238  nnsucsssuc  6460  ecopovtrn  6598  ecopovtrng  6601  addassnqg  7323  distrnqg  7328  ltsonq  7339  ltanqg  7341  ltmnqg  7342  distrnq0  7400  addassnq0  7403  mulasssrg  7699  distrsrg  7700  lttrsr  7703  ltsosr  7705  ltasrg  7711  mulextsr1lem  7721  mulextsr1  7722  axmulass  7814  axdistr  7815  dmdcanap  8618  lt2msq1  8780  ltdiv2  8782  lediv2  8786  xaddass  9805  xaddass2  9806  xlt2add  9816  modqdi  10327  expaddzaplem  10498  expaddzap  10499  expmulzap  10501  resqrtcl  10971  bdtrilem  11180  bdtri  11181  xrbdtri  11217  prmexpb  12083  cnptoprest  12879  ssblps  13065  ssbl  13066  rplogbchbase  13508  rplogbreexp  13511  relogbcxpbap  13523  lgssq  13581