Theorem intnanr 881

Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 3-Apr-1995.)

Hypothesis

Ref	Expression
intnan.1	|- -. ph

Assertion

Ref	Expression
intnanr	|- -. (ph /\ ps)

Proof of Theorem intnanr

Step	Hyp	Ref	Expression
1		intnan.1	. 2 |- -. ph
2		simpl 443	. 2 |- ((ph /\ ps) -> ph)
3	1, 2	mto 167	1 |- -. (ph /\ ps)

This proof depends on syntax axioms:  -. wn 3   /\ 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:  falantru  1338  rab0  3572  co02  5093  fnfreclem2  6319