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Theorem abai 502
Description: Introduce one conjunct as an antecedent to the other. "abai" stands for "and, biconditional, and, implication". (Contributed by NM, 12-Aug-1993.) (Proof shortened by Wolf Lammen, 7-Dec-2012.)
Assertion
Ref Expression
abai ((𝜑𝜓) ↔ (𝜑 ∧ (𝜑𝜓)))

Proof of Theorem abai
StepHypRef Expression
1 biimt 234 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21pm5.32i 435 1 ((𝜑𝜓) ↔ (𝜑 ∧ (𝜑𝜓)))
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:  eu2  1960
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