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Theorem nanbi1d 1453
Description: Introduce a right anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)
Hypothesis
Ref Expression
nanbid.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
nanbi1d (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜃)))

Proof of Theorem nanbi1d
StepHypRef Expression
1 nanbid.1 . 2 (𝜑 → (𝜓𝜒))
2 nanbi1 1447 . 2 ((𝜓𝜒) → ((𝜓𝜃) ↔ (𝜒𝜃)))
31, 2syl 17 1 (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜃)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 195  wnan 1439
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 196  df-an 385  df-nan 1440
This theorem is referenced by: (None)
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