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Theorem anbi1ci 628
Description: Variant of anbi1i 626 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 625 . 2 ((𝜒𝜑) ↔ (𝜒𝜓))
32biancomi 466 1 ((𝜒𝜑) ↔ (𝜓𝜒))
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:  dfid3  5439  imai  5920  wfi  6159  dfac5lem3  9540  cf0  9662  coep  33061  frpoind  33154  brtxp  33415  sscoid  33448  brapply  33473  dfrdg4  33486  wl-df4-3mintru2  34863  rnxrncnvepres  35766  rnxrnidres  35767  pmapglb  37024  polval2N  37160  rp-fakeoranass  40152  alephiso2  40187
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