Theorem intnand 873

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

Hypothesis

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

Assertion

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

Proof of Theorem intnand

Step	Hyp	Ref	Expression
1		intnand.1	. 2 |- ( ph -> -. ps )
2		simpr 108	. 2 |- ( ( ch /\ ps ) -> ps )
3	1, 2	nsyl 590	1 |- ( ph -> -. ( ch /\ ps ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 105  ax-in1 576  ax-in2 577

This theorem is referenced by:  dcan  875  poxp  5873  cauappcvgprlemladdrl  6847  caucvgprlemladdrl  6868  xrrebnd  8886  fzpreddisj  9088  fzp1nel  9121  gcdsupex  10349  gcdsupcl  10350  gcdnncl  10359  gcd2n0cl  10361  qredeu  10479  cncongr2  10486