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

Proof of Theorem intnanrd

Step	Hyp	Ref	Expression
1		intnand.1	. 2 |- ( ph -> -. ps )
2		simpl 107	. 2 |- ( ( ps /\ ch ) -> ps )
3	1, 2	nsyl 590	1 |- ( ph -> -. ( ps /\ ch ) )

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

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-in1 576  ax-in2 577

This theorem is referenced by:  dcan  875  bianfd  889  frecsuclem3  6013  xrrebnd  8886  fzpreddisj  9088  gcdsupex  10349  gcdsupcl  10350  nndvdslegcd  10357  divgcdnn  10366  sqgcd  10418  coprm  10523