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Theorem anabs5 846
Description: Absorption into embedded conjunct. (Contributed by NM, 20-Jul-1996.) (Proof shortened by Wolf Lammen, 9-Dec-2012.)
Assertion
Ref Expression
anabs5 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))

Proof of Theorem anabs5
StepHypRef Expression
1 ibar 523 . . 3 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21bicomd 211 . 2 (𝜑 → ((𝜑𝜓) ↔ 𝜓))
32pm5.32i 666 1 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  axrep5  4694  axsep2  4700  bj-axrep5  31789  elinintrab  36701  2sb5nd  37596  eelTT1  37755  uun121  37830  uunTT1  37840  uunTT1p1  37841  uunTT1p2  37842  uun111  37852  uun2221  37860  uun2221p1  37861  uun2221p2  37862  2sb5ndVD  37967  2sb5ndALT  37989
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