Theorem sbciedOLD

Description: Obsolete version of sbcied as of 12-Oct-2024. (Contributed by NM, 13-Dec-2014) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	sbciedOLD.1	$$⊢\phi \to A\in V$$
	sbciedOLD.2	$$⊢\left(\phi \wedge x=A\right)\to \left(\psi \leftrightarrow \chi \right)$$
Assertion	sbciedOLD	$$⊢\phi \to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi \leftrightarrow \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbciedOLD.1	$$⊢\phi \to A\in V$$
2		sbciedOLD.2	$$⊢\left(\phi \wedge x=A\right)\to \left(\psi \leftrightarrow \chi \right)$$
3		nfv	$$⊢Ⅎx\phi$$
4		nfvd	$$⊢\phi \to Ⅎx\chi$$
5	1 2 3 4	sbciedf	$$⊢\phi \to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi \leftrightarrow \chi \right)$$