Theorem intnanrd 917

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 10-Jul-2005.)

Hypothesis

Ref	Expression
intnand.1	|- ( ph -> -. ps )

Assertion

Ref	Expression
intnanrd	|- ( ph -> -. ( ps /\ ch ) )

Proof of Theorem intnanrd

Step	Hyp	Ref	Expression
1		intnand.1	. 2 |- ( ph -> -. ps )
2		simpl 108	. 2 |- ( ( ps /\ ch ) -> ps )
3	1, 2	nsyl 617	1 |- ( ph -> -. ( ps /\ ch ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-in1 603  ax-in2 604

This theorem is referenced by:  dcan  918  bianfd  932  frecabcl  6289  frecsuclem  6296  xrrebnd  9595  fzpreddisj  9844  iseqf1olemqk  10260  gcdsupex  11635  gcdsupcl  11636  nndvdslegcd  11643  divgcdnn  11652  sqgcd  11706  coprm  11811  ctiunctlemudc  11939