Theorem intnand 874

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 591	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 577  ax-in2 578

This theorem is referenced by:  dcan  876  poxp  5932  cauappcvgprlemladdrl  7119  caucvgprlemladdrl  7140  xrrebnd  9176  fzpreddisj  9378  fzp1nel  9411  gcdsupex  10729  gcdsupcl  10730  gcdnncl  10739  gcd2n0cl  10741  qredeu  10859  cncongr2  10866  divnumden  10954  divdenle  10955