Theorem intnanrd 841

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 102	. 2 |- ( ( ps /\ ch ) -> ps )
3	1, 2	nsyl 558	1 |- ( ph -> -. ( ps /\ ch ) )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-in1 544  ax-in2 545

This theorem is referenced by:  dcan  842  bianfd  855  frecsuclem3  5990  xrrebnd  8732  fzpreddisj  8933