Theorem intnan 691

Description: Introduction of conjunct inside of a contradiction.

Hypothesis

Ref	Expression
intnan.1	|- -. ph

Assertion

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

Proof of Theorem intnan

Step	Hyp	Ref	Expression
1		intnan.1	. 2 |- -. ph
2		pm3.27 323	. 2 |- ((ps /\ ph) -> ph)
3	1, 2	mto 106	1 |- -. (ps /\ ph)

Syntax hints:  -. wn 2   /\ wa 223

This theorem is referenced by:  axnul2 2706  axnul 2707  imadif 3572  xrltnrt 5529  nltmnft 5535  avril1 8739  helloworld 8741

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 147  df-an 225

Copyright terms: Public domain