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Theorem anabs5 851
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 525 . . 3 (𝜑 → (𝜓 ↔ (𝜑𝜓)))
21bicomd 213 . 2 (𝜑 → ((𝜑𝜓) ↔ 𝜓))
32pm5.32i 669 1 ((𝜑 ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  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 197  df-an 386
This theorem is referenced by:  axrep5  4774  axsep2  4780  bj-axrep5  32776  elinintrab  37709  2sb5nd  38602  eelTT1  38761  uun121  38836  uunTT1  38846  uunTT1p1  38847  uunTT1p2  38848  uun111  38858  uun2221  38866  uun2221p1  38867  uun2221p2  38868  2sb5ndVD  38972  2sb5ndALT  38994
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