Theorem simpll3 1062

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

Assertion

Ref	Expression
simpll3	|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ch )

Proof of Theorem simpll3

Step	Hyp	Ref	Expression
1		simpl3 1026	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ch )
2	1	adantr 276	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ch )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1002

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 1004

This theorem is referenced by:  frirrg  4441  fidceq  7039  fidifsnen  7040  en2eqpr  7080  iunfidisj  7124  ordiso2  7213  addlocpr  7734  aptiprlemu  7838  xltadd1  10084  xlesubadd  10091  icoshftf1o  10199  fztri3or  10247  elfzonelfzo  10448  exp3val  10775  nn0ltexp2  10943  hashun  11039  swrdclg  11197  subcn2  11837  divalglemeuneg  12449  dvdslegcd  12500  lcmledvds  12607  rpdvds  12636  cncongr2  12641  qexpz  12890  iuncld  14804  iscnp4  14907  cnpnei  14908  cnconst2  14922  cnpdis  14931  txcn  14964  blssps  15116  blss  15117  metcnp3  15200  metcnp  15201  lgsfcl2  15700  lgsdir  15729  lgsne0  15732