Theorem simpl3l 1083

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

Assertion

Ref	Expression
simpl3l	|- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ph )

Proof of Theorem simpl3l

Step	Hyp	Ref	Expression
1		simp3l 1056	. 2 |- ( ( ch /\ th /\ ( ph /\ ps ) ) -> ph )
2	1	adantr 276	1 |- ( ( ( ch /\ th /\ ( ph /\ ps ) ) /\ ta ) -> ph )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  tfisi  4734  ltmul1a  8919  ltmul1  8920  lemul1a  9188  xaddass  10271  swrdsbslen  11438  swrdspsleq  11439  dvdsadd2b  12607  dvdsaddre2b  12608  pockthg  13136