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Theorem ancrb 309
Description: Conjoin antecedent to right of consequent. (Contributed by NM, 25-Jul-1999.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
ancrb ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))

Proof of Theorem ancrb
StepHypRef Expression
1 iba 288 . 2 (𝜑 → (𝜓 ↔ (𝜓𝜑)))
21pm5.74i 173 1 ((𝜑𝜓) ↔ (𝜑 → (𝜓𝜑)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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