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Theorem orbi1i 715
Description: Inference adding a right disjunct to both sides of a logical equivalence. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
orbi2i.1 (𝜑𝜓)
Assertion
Ref Expression
orbi1i ((𝜑𝜒) ↔ (𝜓𝜒))

Proof of Theorem orbi1i
StepHypRef Expression
1 orcom 682 . 2 ((𝜑𝜒) ↔ (𝜒𝜑))
2 orbi2i.1 . . 3 (𝜑𝜓)
32orbi2i 714 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
4 orcom 682 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
51, 3, 43bitri 204 1 ((𝜑𝜒) ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wb 103  wo 664
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 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  orbi12i  716  orordi  725  dcan  880  3or6  1259  19.45  1618  sbequilem  1766  unass  3155  frecsuc  6154  elznn0nn  8734
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