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Theorem orbi1i 735
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 700 . 2 ((𝜑𝜒) ↔ (𝜒𝜑))
2 orbi2i.1 . . 3 (𝜑𝜓)
32orbi2i 734 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
4 orcom 700 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
51, 3, 43bitri 205 1 ((𝜑𝜒) ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wb 104  wo 680
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 681
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  orbi12i  736  orordi  745  dcan  901  3or6  1284  19.45  1644  sbequilem  1792  unass  3201  frecsuc  6270  elznn0nn  9022
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