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Theorem anabs7 516
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 17-Nov-2013.)
Assertion
Ref Expression
anabs7 ((𝜓 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))

Proof of Theorem anabs7
StepHypRef Expression
1 simpr 107 . . 3 ((𝜑𝜓) → 𝜓)
21pm4.71ri 378 . 2 ((𝜑𝜓) ↔ (𝜓 ∧ (𝜑𝜓)))
32bicomi 127 1 ((𝜓 ∧ (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: (None)
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