Theorem simpll2 984

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 948	. 2 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ps )
2	1	adantr 271	1 |- ( ( ( ( ph /\ ps /\ ch ) /\ th ) /\ ta ) -> ps )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 925

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-3an 927

This theorem is referenced by:  fidceq  6639  fidifsnen  6640  en2eqpr  6677  iunfidisj  6709  cauappcvgprlemlol  7260  caucvgprlemlol  7283  caucvgprprlemlol  7311  elfzonelfzo  9695  qbtwnre  9722  hashun  10267  subcn2  10754  divalglemex  11254  divalglemeuneg  11255  dvdslegcd  11288  lcmledvds  11384