Theorem pm3.2ni 899

Description: Infer negated disjunction of negated premises. (Contributed by NM, 4-Apr-1995.)

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	. 2 |- -. ph
2		id 22	. . 3 |- ( ph -> ph )
3		pm3.2ni.2	. . . 4 |- -. ps
4	3	pm2.21i 116	. . 3 |- ( ps -> ph )
5	2, 4	jaoi 394	. 2 |- ( ( ph \/ ps ) -> ph )
6	1, 5	mto 188	1 |- -. ( ph \/ ps )

Syntax hints:   -. wn 3   \/ wo 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385

This theorem is referenced by:  snsn0non  5846  canthp1lem2  9475  recgt0ii  10929  xrltnr  11953  pnfnlt  11962  nltmnf  11963  lhop  23779  2lgslem4  25131  axlowdimlem13  25834  3pm3.2ni  31594  nosgnn0  31811  clsk1indlem4  38342  clsk1indlem1  38343  dandysum2p2e4  41165