Theorem nanbi12i 1300

Description: Join two logical equivalences with anti-conjunction. (Contributed by SF, 2-Jan-2018.)

Hypotheses

Ref	Expression
nanbii.1	⊢ (φ ↔ ψ)
nanbi12i.2	⊢ (χ ↔ θ)

Assertion

Ref	Expression
nanbi12i	⊢ ((φ ⊼ χ) ↔ (ψ ⊼ θ))

Proof of Theorem nanbi12i

Step	Hyp	Ref	Expression
1		nanbii.1	. 2 ⊢ (φ ↔ ψ)
2		nanbi12i.2	. 2 ⊢ (χ ↔ θ)
3		nanbi12 1297	. 2 ⊢ (((φ ↔ ψ) ∧ (χ ↔ θ)) → ((φ ⊼ χ) ↔ (ψ ⊼ θ)))
4	1, 2, 3	mp2an 653	1 ⊢ ((φ ⊼ χ) ↔ (ψ ⊼ θ))

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)