New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  sbcbiiOLD GIF version

Theorem sbcbiiOLD 3102
 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 (φψ)
Assertion
Ref Expression
sbcbiiOLD (A V → ([̣A / xφ ↔ [̣A / xψ))

Proof of Theorem sbcbiiOLD
StepHypRef Expression
1 sbcbii.1 . . 3 (φψ)
21sbcbii 3101 . 2 ([̣A / xφ ↔ [̣A / xψ)
32a1i 10 1 (A V → ([̣A / xφ ↔ [̣A / xψ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∈ wcel 1710  [̣wsbc 3046 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 3047 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator