Theorem funALTVeqd

Description: Equality deduction for the function predicate. (Contributed by NM, 23-Feb-2013)

	Ref	Expression
Hypothesis	funALTVeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
Assertion	funALTVeqd	⊢ ( 𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		funALTVeqd.1	⊢ ( 𝜑 → 𝐴 = 𝐵 )
2		funALTVeq	⊢ ( 𝐴 = 𝐵 → ( FunALTV 𝐴 ↔ FunALTV 𝐵 ) )
3	1 2	syl	⊢ ( 𝜑 → ( FunALTV 𝐴 ↔ FunALTV 𝐵 ) )