Theorem pm3.2ni 579

Description: Infer negated disjunction of negated premises.

Hypotheses

Ref	Expression
pm3.2ni.1	|- -. ph
pm3.2ni.2	|- -. ps

Assertion

Ref	Expression
pm3.2ni	|- -. (ph \/ ps)

Proof of Theorem pm3.2ni

Step	Hyp	Ref	Expression
1		pm3.2ni.1	. . 3 |- -. ph
2		pm3.2ni.2	. . 3 |- -. ps
3	1, 2	pm3.2i 285	. 2 |- (-. ph /\ -. ps)
4		ioran 306	. 2 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
5	3, 4	mpbir 190	1 |- -. (ph \/ ps)

Syntax hints:  -. wn 2   \/ wo 222   /\ wa 223

This theorem is referenced by:  opprc1b 2791  tz7.44-2 3920  xrltnrt 5522  pnfnltt 5527  nltmnft 5528  recgt0i 5778

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-or 224  df-an 225

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