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Metamath Proof Explorer

Theorem sbf2

Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005)

		Ref	Expression
	Assertion	sbf2	$⊢ [y/ x] \forall x φ \leftrightarrow \forall x φ$

Step	Hyp	Ref	Expression
1		nfa1	$⊢ Ⅎ x \forall x φ$
2	1	sbf	$⊢ [y/ x] \forall x φ \leftrightarrow \forall x φ$