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Theorem abai 824
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 363 . 2 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21pm5.32i 577 1 ((𝜑𝜓) ↔ (𝜑 ∧ (𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 208  wa 398
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 209  df-an 399
This theorem is referenced by:  pm5.75  1025  exintrbi  1892  dfeumo  2619  eu6  2658  dfeu  2680  r19.29imd  3244  dfss4  4209  choc0  29084
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