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Theorem orbi1i 680
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 647 . 2 ((𝜑𝜒) ↔ (𝜒𝜑))
2 orbi2i.1 . . 3 (𝜑𝜓)
32orbi2i 679 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
4 orcom 647 . 2 ((𝜒𝜓) ↔ (𝜓𝜒))
51, 3, 43bitri 195 1 ((𝜑𝜒) ↔ (𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  wb 98  wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  orbi12i  681  orordi  690  dcan  842  3or6  1218  19.45  1573  sbequilem  1719  unass  3100  frecsuc  5991  elznn0nn  8257
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