Theorem sbcbiiOLD 38741

Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) Obsolete as of 17-Aug-2018. Use sbcbii 3491 instead. (New usage is discouraged.) (Proof modification is discouraged.)

Hypothesis

Ref	Expression
sbcbiiOLD.1	⊢ (𝜑 ↔ 𝜓)

Assertion

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

Proof of Theorem sbcbiiOLD

Step	Hyp	Ref	Expression
1		sbcbiiOLD.1	. . 3 ⊢ (𝜑 ↔ 𝜓)
2	1	sbcbii 3491	. 2 ⊢ ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓)
3	2	a1i 11	1 ⊢ (𝐴 ∈ 𝑉 → ([𝐴 / 𝑥]𝜑 ↔ [𝐴 / 𝑥]𝜓))

Syntax hints:   → wi 4   ↔ wb 196   ∈ wcel 1990  [wsbc 3435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-sbc 3436

This theorem is referenced by:  sbc3orgOLD  38742  sbcssOLD  38756  eqsbc3rVD  39075