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  6296  frecsuclem  6303  xrrebnd  9602  fzpreddisj  9851  iseqf1olemqk  10267  gcdsupex  11646  gcdsupcl  11647  nndvdslegcd  11654  divgcdnn  11663  sqgcd  11717  coprm  11822  ctiunctlemudc  11950