Theorem sbcgOLD 3795

Description: Obsolete version of sbcg 3794 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 1917	. 2 ⊢ Ⅎ𝑥𝜑
2	1	sbcgf 3792	1 ⊢ (𝐴 ∈ 𝑉 → ([𝐴 / 𝑥]𝜑 ↔ 𝜑))

Syntax hints:   → wi 4   ↔ wb 205   ∈ wcel 2106  [wsbc 3715

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-12 2171  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-tru 1542  df-ex 1783  df-nf 1787  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-sbc 3716

This theorem is referenced by: (None)