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Theorem anabs1 652
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 474 . . 3 ((𝜑𝜓) → 𝜑)
21pm4.71i 555 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ 𝜑))
32bicomi 215 1 (((𝜑𝜓) ∧ 𝜑) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 197  wa 384
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 198  df-an 385
This theorem is referenced by:  poirr  5211  frgr3v  27576  uun121p1  39696
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