Theorem simpll2 978

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

Assertion

Ref	Expression
simpll2	|- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ps )

Proof of Theorem simpll2

Step	Hyp	Ref	Expression
1		simpl2 942	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ps )
2	1	adantr 270	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 102   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  fidceq  6354  fidifsnen  6355  en2eqpr  6380  cauappcvgprlemlol  6837  caucvgprlemlol  6860  caucvgprprlemlol  6888  elfzonelfzo  9239  qbtwnre  9265  expival  9478  subcn2  10150  divalglemex  10322  divalglemeuneg  10323  dvdslegcd  10356  lcmledvds  10452