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	$$⊢\phi \to \forall x\phi$$
Assertion	sbh	$$⊢\left[y/x\right]\phi \leftrightarrow \phi$$

Proof

Step	Hyp	Ref	Expression
1		sbh.1	$$⊢\phi \to \forall x\phi$$
2	1	nf5i	$$⊢Ⅎx\phi$$
3	2	sbf	$$⊢\left[y/x\right]\phi \leftrightarrow \phi$$