Theorem mpteq2dvaOLD

Description: Obsolete version of mpteq2dva as of 11-Nov-2024. (Contributed by Scott Fenton, 25-Apr-2012) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	mpteq2dva.1	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
Assertion	mpteq2dvaOLD	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq2dva.1	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
2		nfv	$$⊢Ⅎx\phi$$
3	2 1	mpteq2da	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$