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Theorem pm3.2ni 827
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
StepHypRef Expression
1 pm3.2ni.1 . 2  |-  -.  ph
2 id 19 . . 3  |-  ( ph  ->  ph )
3 pm3.2ni.2 . . . 4  |-  -.  ps
43pm2.21i 123 . . 3  |-  ( ps 
->  ph )
52, 4jaoi 368 . 2  |-  ( (
ph  \/  ps )  ->  ph )
61, 5mto 167 1  |-  -.  ( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357
This theorem is referenced by:  snsn0non  4511  canthp1lem2  8275  recgt0ii  9662  xrltnr  10462  pnfnlt  10467  nltmnf  10468  lhop  19363  3pm3.2ni  24064  nosgnn0  24312  axlowdimlem13  24582  dandysum2p2e4  27943
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
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