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Theorem anabs5 568
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
anabs5 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))

Proof of Theorem anabs5
StepHypRef Expression
1 ibar 299 . . 3 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21bicomd 140 . 2 (𝜑 → ((𝜑𝜓) ↔ 𝜓))
32pm5.32i 451 1 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wa 103  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mo3h  2072  indif  3370  axsep2  4106
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