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Theorem anabs7 785
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 17-Nov-2013.)
Assertion
Ref Expression
anabs7 ((ψ (φ ψ)) ↔ (φ ψ))

Proof of Theorem anabs7
StepHypRef Expression
1 simpr 447 . . 3 ((φ ψ) → ψ)
21pm4.71ri 614 . 2 ((φ ψ) ↔ (ψ (φ ψ)))
32bicomi 193 1 ((ψ (φ ψ)) ↔ (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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