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Theorem wl-nanbi1 33430
Description: Introduce a right anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.) (Revised by Wolf Lammen, 27-Jun-2020.)
Assertion
Ref Expression
wl-nanbi1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))

Proof of Theorem wl-nanbi1
StepHypRef Expression
1 imbi1 336 . 2 ((𝜑𝜓) → ((𝜑 → ¬ 𝜒) ↔ (𝜓 → ¬ 𝜒)))
2 wl-dfnan2 33426 . 2 ((𝜑𝜒) ↔ (𝜑 → ¬ 𝜒))
3 wl-dfnan2 33426 . 2 ((𝜓𝜒) ↔ (𝜓 → ¬ 𝜒))
41, 2, 33bitr4g 303 1 ((𝜑𝜓) → ((𝜑𝜒) ↔ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wnan 1487
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 385  df-nan 1488
This theorem is referenced by: (None)
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