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Theorem anabs1 506
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 102 . . 3 ((𝜑𝜓) → 𝜑)
21pm4.71i 371 . 2 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ 𝜑))
32bicomi 123 1 (((𝜑𝜓) ∧ 𝜑) ↔ (𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  wa 97  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  poirr  4041
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