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Theorem biorf 394
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 373 . 2 (ψ → (φ ψ))
2 orel1 371 . 2 φ → ((φ ψ) → ψ))
31, 2impbid2 195 1 φ → (ψ ↔ (φ ψ)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wo 357
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359
This theorem is referenced by:  biortn  395  pm5.61  693  pm5.55  867  cadan  1392  euor  2231  eueq3  3011  unineq  3505  ifor  3702  difprsnss  3846  eqtfinrelk  4486  dfphi2  4569
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