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Theorem orbi1i 713
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 680 . 2  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
2 orbi2i.1 . . 3  |-  ( ph  <->  ps )
32orbi2i 712 . 2  |-  ( ( ch  \/  ph )  <->  ( ch  \/  ps )
)
4 orcom 680 . 2  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
51, 3, 43bitri 204 1  |-  ( (
ph  \/  ch )  <->  ( ps  \/  ch )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  orbi12i  714  orordi  723  dcan  876  3or6  1255  19.45  1614  sbequilem  1761  unass  3141  frecsuc  6103  elznn0nn  8659
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