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Theorem rbaibr 541
Description: Move conjunction outside of biconditional. (Contributed by Mario Carneiro, 11-Sep-2015.) (Proof shortened by Wolf Lammen, 19-Jan-2020.)
Hypothesis
Ref Expression
baib.1 (𝜑 ↔ (𝜓𝜒))
Assertion
Ref Expression
rbaibr (𝜒 → (𝜓𝜑))

Proof of Theorem rbaibr
StepHypRef Expression
1 baib.1 . . 3 (𝜑 ↔ (𝜓𝜒))
21biancomi 466 . 2 (𝜑 ↔ (𝜒𝜓))
32baibr 540 1 (𝜒 → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  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:  rbaib  542  exintrbi  1892  moeuex  2645  sssseq  3936  ssunsn2  4723  sdrgacs  19576  cmpfi  22016  nanorxor  40996
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