Theorem funALTVeqd

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

	Ref	Expression
Hypothesis	funALTVeqd.1	$$⊢\phi \to A=B$$
Assertion	funALTVeqd	$$⊢\phi \to \left(FunALTVA\leftrightarrow FunALTVB\right)$$

Proof

Step	Hyp	Ref	Expression
1		funALTVeqd.1	$$⊢\phi \to A=B$$
2		funALTVeq	$$⊢A=B\to \left(FunALTVA\leftrightarrow FunALTVB\right)$$
3	1 2	syl	$$⊢\phi \to \left(FunALTVA\leftrightarrow FunALTVB\right)$$