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Theorem anabs7 643
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 471 . . 3 ((𝜑𝜓) → 𝜓)
21pm4.71ri 550 . 2 ((𝜑𝜓) ↔ (𝜓 ∧ (𝜑𝜓)))
32bicomi 214 1 ((𝜓 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 382
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 197  df-an 383
This theorem is referenced by:  prtlem15  34683  un2122  39542
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