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Theorem rbaibr 943
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 iba 522 . 2 (𝜒 → (𝜓 ↔ (𝜓𝜒)))
2 baib.1 . 2 (𝜑 ↔ (𝜓𝜒))
31, 2syl6bbr 276 1 (𝜒 → (𝜓𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wa 382
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 195  df-an 384
This theorem is referenced by:  rbaib  944  exintrbi  1807  ssunsn2  4296  cmpfi  20963  sdrgacs  36586  nanorxor  37322  sssseq  40103
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