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Theorem anbi1 687
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) → ((φ χ) ↔ (ψ χ)))

Proof of Theorem anbi1
StepHypRef Expression
1 id 19 . 2 ((φψ) → (φψ))
21anbi1d 685 1 ((φψ) → ((φ χ) ↔ (ψ χ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wa 358
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 177  df-an 360
This theorem is referenced by:  pm5.75  903  nanbi1  1295
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