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Metamath Proof Explorer

Theorem sbh

Description: Substitution for a variable not free in a wff does not affect it. (Contributed by NM, 14-May-1993)

		Ref	Expression
	Hypothesis	sbh.1	$⊢ φ \to \forall x φ$
	Assertion	sbh	$⊢ [y/ x] φ \leftrightarrow φ$

Step	Hyp	Ref	Expression
1		sbh.1	$⊢ φ \to \forall x φ$
2	1	nf5i	$⊢ Ⅎ x φ$
3	2	sbf	$⊢ [y/ x] φ \leftrightarrow φ$