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Theorem an21 632
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 ancom 453 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
21anbi1i 615 . 2 (((𝜑𝜓) ∧ 𝜒) ↔ ((𝜓𝜑) ∧ 𝜒))
3 anass 461 . 2 (((𝜓𝜑) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
42, 3bitri 267 1 (((𝜑𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 198  wa 387
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 199  df-an 388
This theorem is referenced by:  an12  633  fncnv  6265  mpocurryd  7744  rexuz2  12119  logfac2  25510  ltgov  26100  brimg  32959  eldmqsres  35027  xrninxp2  35126
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