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Theorem nanbi12i 1452
Description: Join two logical equivalences with anti-conjunction. (Contributed by SF, 2-Jan-2018.)
Hypotheses
Ref Expression
nanbii.1 (𝜑𝜓)
nanbi12i.2 (𝜒𝜃)
Assertion
Ref Expression
nanbi12i ((𝜑𝜒) ↔ (𝜓𝜃))

Proof of Theorem nanbi12i
StepHypRef Expression
1 nanbii.1 . 2 (𝜑𝜓)
2 nanbi12i.2 . 2 (𝜒𝜃)
3 nanbi12 1449 . 2 (((𝜑𝜓) ∧ (𝜒𝜃)) → ((𝜑𝜒) ↔ (𝜓𝜃)))
41, 2, 3mp2an 704 1 ((𝜑𝜒) ↔ (𝜓𝜃))
Colors of variables: wff setvar class
Syntax hints:  wb 195  wnan 1439
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 196  df-an 385  df-nan 1440
This theorem is referenced by: (None)
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