Theorem sbcbiiOLD 3103

Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
sbcbii.1	⊢ (φ ↔ ψ)

Assertion

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

Proof of Theorem sbcbiiOLD

Step	Hyp	Ref	Expression
1		sbcbii.1	. . 3 ⊢ (φ ↔ ψ)
2	1	sbcbii 3102	. 2 ⊢ ([̣A / x]̣φ ↔ [̣A / x]̣ψ)
3	2	a1i 10	1 ⊢ (A ∈ V → ([̣A / x]̣φ ↔ [̣A / x]̣ψ))

Syntax hints:   → wi 4   ↔ wb 176   ∈ wcel 1710  [̣wsbc 3047

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-sbc 3048

This theorem is referenced by: (None)