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Theorem orbi1i 679
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 ((φ χ) ↔ (ψ χ))

Proof of Theorem orbi1i
StepHypRef Expression
1 orcom 646 . 2 ((φ χ) ↔ (χ φ))
2 orbi2i.1 . . 3 (φψ)
32orbi2i 678 . 2 ((χ φ) ↔ (χ ψ))
4 orcom 646 . 2 ((χ ψ) ↔ (ψ χ))
51, 3, 43bitri 195 1 ((φ χ) ↔ (ψ χ))
Colors of variables: wff set class
Syntax hints:  wb 98   wo 628
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 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  orbi12i  680  orordi  689  dcan  841  3or6  1217  19.45  1570  sbequilem  1716  unass  3094  frecsuc  5930  elznn0nn  8035
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