Theorem intnanr 695

Description: Introduction of conjunct inside of a contradiction.

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		pm3.26 317	. 2 |- ((ph /\ ps) -> ph)
3	1, 2	mto 105	1 |- -. (ph /\ ps)

Syntax hints:  -. wn 2   /\ wa 221

This theorem is referenced by:  rab0 2338  0nelxp 3299  co02 3582  xrltnr 5630  pnfnlt 5635  nltmnf 5636  ruclem29 7663

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 145  df-an 223

Copyright terms: Public domain