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Theorem nanbi2i 1456
Description: Introduce a left anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)
Hypothesis
Ref Expression
nanbii.1 (𝜑𝜓)
Assertion
Ref Expression
nanbi2i ((𝜒𝜑) ↔ (𝜒𝜓))

Proof of Theorem nanbi2i
StepHypRef Expression
1 nanbii.1 . 2 (𝜑𝜓)
2 nanbi2 1453 . 2 ((𝜑𝜓) → ((𝜒𝜑) ↔ (𝜒𝜓)))
31, 2ax-mp 5 1 ((𝜒𝜑) ↔ (𝜒𝜓))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wnan 1444
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 197  df-an 386  df-nan 1445
This theorem is referenced by:  nabi2i  32069  rp-fakenanass  37376
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