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Metamath Proof Explorer

Theorem nfsbc1

Description: Bound-variable hypothesis builder for class substitution. (Contributed by NM, 5-Aug-1993) (Revised by Mario Carneiro, 12-Oct-2016)

		Ref	Expression
	Hypothesis	nfsbc1.1	$⊢ \underline{Ⅎ} x A$
	Assertion	nfsbc1	$⊢ Ⅎ x \underset{˙}{[} A / x \underset{˙}{]} φ$

Step	Hyp	Ref	Expression
1		nfsbc1.1	$⊢ \underline{Ⅎ} x A$
2	1	a1i	$⊢ ⊤ \to \underline{Ⅎ} x A$
3	2	nfsbc1d	$⊢ ⊤ \to Ⅎ x \underset{˙}{[} A / x \underset{˙}{]} φ$
4	3	mptru	$⊢ Ⅎ x \underset{˙}{[} A / x \underset{˙}{]} φ$