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Theorem anabs1 783
Description: Absorption into embedded conjunct. (Contributed by NM, 4-Sep-1995.) (Proof shortened by Wolf Lammen, 16-Nov-2013.)
Assertion
Ref Expression
anabs1 (((φ ψ) φ) ↔ (φ ψ))

Proof of Theorem anabs1
StepHypRef Expression
1 simpl 443 . . 3 ((φ ψ) → φ)
21pm4.71i 613 . 2 ((φ ψ) ↔ ((φ ψ) φ))
32bicomi 193 1 (((φ ψ) φ) ↔ (φ ψ))
Colors of variables: wff setvar class
Syntax hints:  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by: (None)
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