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 → ∀ 𝑥 𝜑 )
Assertion	sbh	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 ↔ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		sbh.1	⊢ ( 𝜑 → ∀ 𝑥 𝜑 )
2	1	nf5i	⊢ Ⅎ 𝑥 𝜑
3	2	sbf	⊢ ( [ 𝑦 / 𝑥 ] 𝜑 ↔ 𝜑 )