Theorem sbh 2272

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

Hypothesis

Ref	Expression
sbh.1	⊢ (𝜑 → ∀𝑥𝜑)

Assertion

Ref	Expression
sbh	⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Proof of Theorem sbh

Step	Hyp	Ref	Expression
1		sbh.1	. . 3 ⊢ (𝜑 → ∀𝑥𝜑)
2	1	nf5i 2145	. 2 ⊢ Ⅎ𝑥𝜑
3	2	sbf 2270	1 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1537  [wsb 2063

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-10 2140  ax-12 2176

This theorem depends on definitions:  df-bi 207  df-ex 1779  df-nf 1783  df-sb 2064

This theorem is referenced by: (None)