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Theorem bianbi 626
Description: Exchanging conjunction in a biconditional. (Contributed by Peter Mazsa, 31-Jul-2023.)
Hypotheses
Ref Expression
bianbi.1 (𝜑 ↔ (𝜓𝜒))
bianbi.2 (𝜓𝜃)
Assertion
Ref Expression
bianbi (𝜑 ↔ (𝜃𝜒))

Proof of Theorem bianbi
StepHypRef Expression
1 bianbi.1 . 2 (𝜑 ↔ (𝜓𝜒))
2 bianbi.2 . . 3 (𝜓𝜃)
32anbi1i 623 . 2 ((𝜓𝜒) ↔ (𝜃𝜒))
41, 3bitri 275 1 (𝜑 ↔ (𝜃𝜒))
Colors of variables: wff setvar class
Syntax hints:  wb 205  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 206  df-an 396
This theorem is referenced by:  anbi12i  627  bianassc  642  pm5.53  1003  dfifp4  1065  dfifp5  1066  an3andi  1479  19.28v  1987  19.28  2217  2eu4  2646  r19.26-3  3109  3reeanv  3224  rmo4  3725  rmo3f  3729  sbc3an  3846  rmo3  3882  difin2  4292  otelxp  5722  dfrefrel5  37989  dfantisymrel4  38233  dfantisymrel5  38234  grimuhgr  47176
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