Theorem sbcbi2OLD 3835

Description: Obsolete proof of sbcbi2 3834 as of 5-May-2024. (Contributed by Giovanni Mascellani, 9-Apr-2018.) (Proof shortened by Wolf Lammen, 4-May-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
sbcbi2OLD	⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓))

Proof of Theorem sbcbi2OLD

Step	Hyp	Ref	Expression
1		nfa1 2140	. 2 ⊢ Ⅎ𝑥∀𝑥(𝜑 ↔ 𝜓)
2		sp 2168	. 2 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → (𝜑 ↔ 𝜓))
3	1, 2	sbcbid 3830	1 ⊢ (∀𝑥(𝜑 ↔ 𝜓) → ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓))

Syntax hints:   → wi 4   ↔ wb 205  ∀wal 1531  [wsbc 3772

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-12 2163  ax-ext 2697

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-sbc 3773

This theorem is referenced by: (None)