Theorem intnanr 756

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		simpl 346	. 2 |- ((ph /\ ps) -> ph)
3	1, 2	mto 121	1 |- -. (ph /\ ps)

Syntax hints:  -. wn 2   /\ wa 240

This theorem is referenced by:  rab0 2894  rab0OLD 2895  0nelxp 4066  co02 4411  xrltnr 6716  pnfnlt 6721  nltmnf 6722  ruclem29 8807  FTAid 14108  zrfld 14784  padd02 17273

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 164  df-an 242

Copyright terms: Public domain