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Theorem iba 294
Description: Introduction of antecedent as conjunct. Theorem *4.73 of [WhiteheadRussell] p. 121. (Contributed by NM, 30-Mar-1994.) (Revised by NM, 24-Mar-2013.)
Assertion
Ref Expression
iba (𝜑 → (𝜓 ↔ (𝜓𝜑)))

Proof of Theorem iba
StepHypRef Expression
1 pm3.21 260 . 2 (𝜑 → (𝜓 → (𝜓𝜑)))
2 simpl 107 . 2 ((𝜓𝜑) → 𝜓)
31, 2impbid1 140 1 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 102  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  biantru  296  biantrud  298  ancrb  315  rbaibd  867  dedlem0a  910  fvopab6  5317  fressnfv  5403  tpostpos  5934  nnmword  6179  unfiexmid  6463  ltmpig  6627
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