Theorem nanbi1i 1298

Description: Introduce a right anti-conjunct to both sides of a logical equivalence. (Contributed by SF, 2-Jan-2018.)

Hypothesis

Ref	Expression
nanbii.1	⊢ (φ ↔ ψ)

Assertion

Ref	Expression
nanbi1i	⊢ ((φ ⊼ χ) ↔ (ψ ⊼ χ))

Proof of Theorem nanbi1i

Step	Hyp	Ref	Expression
1		nanbii.1	. 2 ⊢ (φ ↔ ψ)
2		nanbi1 1295	. 2 ⊢ ((φ ↔ ψ) → ((φ ⊼ χ) ↔ (ψ ⊼ χ)))
3	1, 2	ax-mp 5	1 ⊢ ((φ ⊼ χ) ↔ (ψ ⊼ χ))

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)