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Theorem bi3impb 39006
Description: Similar to 3impb 1279 with implication in hypothesis replaced by biconditional. (Contributed by Alan Sare, 6-Nov-2017.)
Hypothesis
Ref Expression
bi3impb.1 ((𝜑 ∧ (𝜓𝜒)) ↔ 𝜃)
Assertion
Ref Expression
bi3impb ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem bi3impb
StepHypRef Expression
1 bi3impb.1 . . 3 ((𝜑 ∧ (𝜓𝜒)) ↔ 𝜃)
21biimpi 206 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323impb 1279 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383  w3a 1054
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 197  df-an 385  df-3an 1056
This theorem is referenced by: (None)
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