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Theorem iba 489
Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.)
Assertion
Ref Expression
iba (φ → (ψ ↔ (ψ φ)))

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 435 . 2 (φ → (ψ → (ψ φ)))
2 simpl 443 . 2 ((ψ φ) → ψ)
31, 2impbid1 194 1 (φ → (ψ ↔ (ψ φ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  biantru  491  biantrud  493  ancrb  533  pm5.54  870  rbaibd  876  dedlem0a  918  unineq  3505  dfphi2  4569  opres  4978  resieq  4979  cores  5084  fvres  5342  fressnfv  5439  epelcres  6328
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