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Theorem nanbi1d 1301
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 → ((ψ θ) ↔ (χ θ)))

Proof of Theorem nanbi1d
StepHypRef Expression
1 nanbid.1 . 2 (φ → (ψχ))
2 nanbi1 1295 . 2 ((ψχ) → ((ψ θ) ↔ (χ θ)))
31, 2syl 15 1 (φ → ((ψ θ) ↔ (χ θ)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   wnan 1287
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  df-nan 1288
This theorem is referenced by:  nineq1  3235
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