Theorem intnand 882

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 447	. 2 |- ((ch /\ ps) -> ps)
3	1, 2	nsyl 113	1 |- (ph -> -. (ch /\ ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  nnadjoinpw  4522  nmembers1lem3  6271