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Theorem nanbi1i 1298
Description: Introduce a right anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)
Hypothesis
Ref Expression
nanbii.1 (φψ)
Assertion
Ref Expression
nanbi1i ((φ χ) ↔ (ψ χ))

Proof of Theorem nanbi1i
StepHypRef Expression
1 nanbii.1 . 2 (φψ)
2 nanbi1 1295 . 2 ((φψ) → ((φ χ) ↔ (ψ χ)))
31, 2ax-mp 5 1 ((φ χ) ↔ (ψ χ))
Colors of variables: wff setvar class
Syntax hints:  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: (None)
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