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Theorem an21 643
Description: Swap two conjuncts. (Contributed by Peter Mazsa, 18-Sep-2022.)
Assertion
Ref Expression
an21 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))

Proof of Theorem an21
StepHypRef Expression
1 biid 264 . . 3 ((𝜑𝜒) ↔ (𝜑𝜒))
21bianassc 642 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ ((𝜑𝜓) ∧ 𝜒))
32bicomi 227 1 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 209  wa 399
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 210  df-an 400
This theorem is referenced by:  an32  645  an13  646  fncnv  6397  mpocurryd  7918  rexuz2  12287  resmndismnd  17965  logfac2  25801  ltgov  26391  brimg  33511  eldmqsres  35703  xrninxp2  35801
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