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Theorem orbi1i 690
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 657 . 2  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
2 orbi2i.1 . . 3  |-  ( ph  <->  ps )
32orbi2i 689 . 2  |-  ( ( ch  \/  ph )  <->  ( ch  \/  ps )
)
4 orcom 657 . 2  |-  ( ( ch  \/  ps )  <->  ( ps  \/  ch )
)
51, 3, 43bitri 199 1  |-  ( (
ph  \/  ch )  <->  ( ps  \/  ch )
)
Colors of variables: wff set class
Syntax hints:    <-> wb 102    \/ wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  orbi12i  691  orordi  700  dcan  853  3or6  1229  19.45  1589  sbequilem  1735  unass  3127  frecsuc  6021  elznn0nn  8315
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