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Theorem an21 641
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 260 . . 3 ((𝜑𝜒) ↔ (𝜑𝜒))
21bianassc 640 . 2 ((𝜓 ∧ (𝜑𝜒)) ↔ ((𝜑𝜓) ∧ 𝜒))
32bicomi 223 1 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 205  wa 396
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 206  df-an 397
This theorem is referenced by:  an32  643  an13  644  indifdi  4230  fncnv  6557  mpocurryd  8155  rexuz2  12740  resmndismnd  18544  logfac2  26471  ltgov  27247  brimg  34335  eldmqsres  36552  xrninxp2  36660
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