Theorem simp1l 1023

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 109	. 2 |- ( ( ph /\ ps ) -> ph )
2	1	3ad2ant1 1020	1 |- ( ( ( ph /\ ps ) /\ ch /\ th ) -> ph )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 980

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 982

This theorem is referenced by:  simpl1l  1050  simpr1l  1056  simp11l  1110  simp21l  1116  simp31l  1122  en2lp  4586  tfisi  4619  funprg  5304  nnsucsssuc  6545  ecopovtrn  6686  ecopovtrng  6689  addassnqg  7442  distrnqg  7447  ltsonq  7458  ltanqg  7460  ltmnqg  7461  distrnq0  7519  addassnq0  7522  mulasssrg  7818  distrsrg  7819  lttrsr  7822  ltsosr  7824  ltasrg  7830  mulextsr1lem  7840  mulextsr1  7841  axmulass  7933  axdistr  7934  dmdcanap  8741  lt2msq1  8904  ltdiv2  8906  lediv2  8910  xaddass  9935  xaddass2  9936  xlt2add  9946  modqdi  10463  expaddzaplem  10653  expaddzap  10654  expmulzap  10656  resqrtcl  11173  bdtrilem  11382  bdtri  11383  xrbdtri  11419  prmexpb  12289  4sqlem18  12546  subgabl  13402  opprringbg  13576  cnptoprest  14407  ssblps  14593  ssbl  14594  plyadd  14897  plymul  14898  rplogbchbase  15082  rplogbreexp  15085  relogbcxpbap  15097  lgssq  15156