Theorem sbcgOLD 3874

Description: Obsolete version of sbcg 3873 as of 12-Oct-2024. (Contributed by Alan Sare, 10-Nov-2012.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
sbcgOLD	⊢ (𝐴 ∈ 𝑉 → ([𝐴 / 𝑥]𝜑 ↔ 𝜑))

Distinct variable group:   𝜑,𝑥

Allowed substitution hints:   𝐴(𝑥)   𝑉(𝑥)

Proof of Theorem sbcgOLD

Step	Hyp	Ref	Expression
1		nfv 1914	. 2 ⊢ Ⅎ𝑥𝜑
2	1	sbcgf 3871	1 ⊢ (𝐴 ∈ 𝑉 → ([𝐴 / 𝑥]𝜑 ↔ 𝜑))

Syntax hints:   → wi 4   ↔ wb 206   ∈ wcel 2108  [wsbc 3794

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 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-12 2177  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-nf 1783  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-sbc 3795

This theorem is referenced by: (None)