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Theorem nanbi12d 1454
Description: Join two logical equivalences with anti-conjunction. (Contributed by Scott Fenton, 2-Jan-2018.)
Hypotheses
Ref Expression
nanbid.1 (𝜑 → (𝜓𝜒))
nanbi12d.2 (𝜑 → (𝜃𝜏))
Assertion
Ref Expression
nanbi12d (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜏)))

Proof of Theorem nanbi12d
StepHypRef Expression
1 nanbid.1 . 2 (𝜑 → (𝜓𝜒))
2 nanbi12d.2 . 2 (𝜑 → (𝜃𝜏))
3 nanbi12 1448 . 2 (((𝜓𝜒) ∧ (𝜃𝜏)) → ((𝜓𝜃) ↔ (𝜒𝜏)))
41, 2, 3syl2anc 690 1 (𝜑 → ((𝜓𝜃) ↔ (𝜒𝜏)))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 194  wnan 1438
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 195  df-an 384  df-nan 1439
This theorem is referenced by:  rp-fakenanass  36675
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