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Theorem anbi2 746
Description: Introduce a left conjunct to both sides of a logical equivalence. (Contributed by NM, 16-Nov-2013.)
Assertion
Ref Expression
anbi2 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))

Proof of Theorem anbi2
StepHypRef Expression
1 id 22 . 2 ((𝜑𝜓) → (𝜑𝜓))
21anbi2d 742 1 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wa 383
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
This theorem is referenced by:  eleq2d  2826  anbi1cd  34342
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