Theorem sbcbii

Description: Formula-building inference for class substitution. (Contributed by NM, 11-Nov-2005)

	Ref	Expression
Hypothesis	sbcbii.1	$$⊢\phi \leftrightarrow \psi$$
Assertion	sbcbii	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi$$

Proof

Step	Hyp	Ref	Expression
1		sbcbii.1	$$⊢\phi \leftrightarrow \psi$$
2	1	a1i	$$⊢\top \to \left(\phi \leftrightarrow \psi \right)$$
3	2	sbcbidv	$$⊢\top \to \left(\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi \right)$$
4	3	mptru	$$⊢\underset{\dot{}}{[}A/x\underset{\dot{}}{]}\phi \leftrightarrow \underset{\dot{}}{[}A/x\underset{\dot{}}{]}\psi$$