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Theorem anabs5 515
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 289 . . 3 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21bicomd 133 . 2 (𝜑 → ((𝜑𝜓) ↔ 𝜓))
32pm5.32i 435 1 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  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:  mo3h  1969  indif  3207  axsep2  3903
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