Theorem sbh 2274

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 2147	. 2 ⊢ Ⅎ𝑥𝜑
3	2	sbf 2272	1 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑)

Syntax hints:   → wi 4   ↔ wb 206  ∀wal 1538  [wsb 2065

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-10 2142  ax-12 2178

This theorem depends on definitions:  df-bi 207  df-ex 1780  df-nf 1784  df-sb 2066

This theorem is referenced by: (None)