Theorem sbh 2284

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 2157	. 2 ⊢ Ⅎ𝑥𝜑
3	2	sbf 2282	1 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 207  ∀wal 1545  [wsb 2073

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-10 2152  ax-12 2189

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787  df-nf 1791  df-sb 2074

This theorem is referenced by: (None)