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Theorem orbi1i 752
Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
orbi2i.1  |-  ( ph  <->  ps )
Assertion
Ref Expression
orbi1i  |-  ( (
ph  \/  ch )  <->  ( ps  \/  ch )
)

Proof of Theorem orbi1i
StepHypRef Expression
1 orcom 717 . 2  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
2 orbi2i.1 . . 3  |-  ( ph  <->  ps )
32orbi2i 751 . 2  |-  ( ( ch  \/  ph )  <->  ( ch  \/  ps )
)
4 orcom 717 . 2  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
51, 3, 43bitri 205 1  |-  ( (
ph  \/  ch )  <->  ( ps  \/  ch )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  orbi12i  753  orordi  762  dcan  918  3or6  1301  19.45  1661  sbequilem  1810  unass  3233  frecsuc  6304  elznn0nn  9075
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