MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  anbi1ci Structured version   Visualization version   GIF version

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  5581  imai  6092  frpoind  6363  wfiOLD  6372  dfac5lem3  10165  cf0  10291  eqscut2  27851  coep  35752  brtxp  35881  sscoid  35914  brapply  35939  dfrdg4  35952  wl-df4-3mintru2  37488  rnxrncnvepres  38401  rnxrnidres  38402  pmapglb  39772  polval2N  39908  rp-fakeoranass  43527  alephiso2  43571
  Copyright terms: Public domain W3C validator