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Theorem a1bi 241
Description: Inference rule introducing a theorem as an antecedent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 11-Nov-2012.)
Hypothesis
Ref Expression
a1bi.1 𝜑
Assertion
Ref Expression
a1bi (𝜓 ↔ (𝜑𝜓))

Proof of Theorem a1bi
StepHypRef Expression
1 a1bi.1 . 2 𝜑
2 biimt 239 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
31, 2ax-mp 7 1 (𝜓 ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  mt2bi  642  truimfal  1342  equsal  1656  equveli  1683  ralv  2617  relop  4514
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