Theorem simpll1 1062

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

Assertion

Ref	Expression
simpll1	|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ph )

Proof of Theorem simpll1

Step	Hyp	Ref	Expression
1		simpl1 1026	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ph )
2	1	adantr 276	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ph )

Syntax hints:   -> wi 4   /\ wa 104   /\ w3a 1004

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

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  fidifsnen  7057  ordiso2  7234  ctssdc  7312  addlocpr  7756  xltadd1  10111  nn0ltexp2  10972  hashun  11069  fimaxq  11092  xrmaxltsup  11836  dvdslegcd  12553  lcmledvds  12660  divgcdcoprm0  12691  rpexp  12743  qexpz  12943  dfgrp3mlem  13699  rhmdvdsr  14208  rnglidlmcl  14513  iscnp4  14961  cnconst2  14976  blssps  15170  blss  15171  metcnp  15255  addcncntoplem  15304  cdivcncfap  15347  lgsfvalg  15753  lgsmod  15774  lgsdir  15783  lgsne0  15786  clwwlknonex2  16309  eulerpathum  16351