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Theorem biorf 662
Description: A wff is equivalent to its disjunction with falsehood. Theorem *4.74 of [WhiteheadRussell] p. 121. (Contributed by NM, 23-Mar-1995.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)
Assertion
Ref Expression
biorf φ → (ψ ↔ (φ ψ)))

Proof of Theorem biorf
StepHypRef Expression
1 olc 631 . 2 (ψ → (φ ψ))
2 orel1 643 . 2 φ → ((φ ψ) → ψ))
31, 2impbid2 131 1 φ → (ψ ↔ (φ ψ)))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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-in2 545  ax-io 629
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  biortn  663  pm5.61  707  pm5.55dc  818  euor  1923  eueq3dc  2709  difprsnss  3493  opthprc  4334  frecsuclem3  5929  swoord1  6071  indpi  6326  enq0tr  6416  mulap0r  7359  mulge0  7363
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