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Theorem anabs1 659
Description: Absorption into embedded conjunct. (Contributed by NM, 4-Sep-1995.) (Proof shortened by Wolf Lammen, 16-Nov-2013.)
Assertion
Ref Expression
anabs1 (((𝜑𝜓) ∧ 𝜑) ↔ (𝜑𝜓))

Proof of Theorem anabs1
StepHypRef Expression
1 simpl 483 . . 3 ((𝜑𝜓) → 𝜑)
21pm4.71i 560 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ 𝜑))
32bicomi 223 1 (((𝜑𝜓) ∧ 𝜑) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396
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 206  df-an 397
This theorem is referenced by:  3anidm  1103  poirr  5511  frgr3v  28625  uun121p1  42363
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