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Theorem anbi1ci 626
Description: Variant of anbi1i 624 with commutation. (Contributed by Peter Mazsa, 7-Mar-2020.)
Hypothesis
Ref Expression
anbi.1 (𝜑𝜓)
Assertion
Ref Expression
anbi1ci ((𝜒𝜑) ↔ (𝜓𝜒))

Proof of Theorem anbi1ci
StepHypRef Expression
1 anbi.1 . . 3 (𝜑𝜓)
21anbi2i 623 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
32biancomi 462 1 ((𝜒𝜑) ↔ (𝜓𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 206  wa 395
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 207  df-an 396
This theorem is referenced by:  dfid3  5586  imai  6094  frpoind  6365  wfiOLD  6374  dfac5lem3  10163  cf0  10289  eqscut2  27866  coep  35732  brtxp  35862  sscoid  35895  brapply  35920  dfrdg4  35933  wl-df4-3mintru2  37470  rnxrncnvepres  38382  rnxrnidres  38383  pmapglb  39753  polval2N  39889  rp-fakeoranass  43504  alephiso2  43548
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