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Theorem anbi2 448
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 19 . 2 ((𝜑𝜓) → (𝜑𝜓))
21anbi2d 445 1 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  ifbi  3375
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