Theorem sbcbi2OLD

Description: Obsolete proof of sbcbi2 as of 5-May-2024. (Contributed by Giovanni Mascellani, 9-Apr-2018) (Proof shortened by Wolf Lammen, 4-May-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	sbcbi2OLD	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfa1	$$⊢Ⅎx\forall x\left(\phi \leftrightarrow \psi \right)$$
2		sp	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$
3	1 2	sbcbid	$$⊢\forall x\left(\phi \leftrightarrow \psi \right)\to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi \right)$$