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Theorem anbi1 447
Description: Introduce a right conjunct to both sides of a logical equivalence. Theorem *4.36 of [WhiteheadRussell] p. 118. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
anbi1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))

Proof of Theorem anbi1
StepHypRef Expression
1 id 19 . 2 ((𝜑𝜓) → (𝜑𝜓))
21anbi1d 446 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
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:  pm5.75  880  expap0  9444
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