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Theorem orci 685
Description: Deduction introducing a disjunct. (Contributed by NM, 19-Jan-2008.) (Revised by Mario Carneiro, 31-Jan-2015.)
Hypothesis
Ref Expression
orci.1  |-  ph
Assertion
Ref Expression
orci  |-  ( ph  \/  ps )

Proof of Theorem orci
StepHypRef Expression
1 orci.1 . 2  |-  ph
2 orc 668 . 2  |-  ( ph  ->  ( ph  \/  ps ) )
31, 2ax-mp 7 1  |-  ( ph  \/  ps )
Colors of variables: wff set class
Syntax hints:    \/ wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  truorfal  1342  prid1g  3541  onsucelsucexmidlem1  4334  regexmidlemm  4338  nn0suc  4409  nndceq0  4421  0elnn  4422  acexmidlem2  5631  indpi  6880  nn1gt1  8427  nneoor  8818  mnfltpnf  9224  bcpasc  10139
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