Users' Mathboxes Mathbox for Alan Sare < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcbiiOLD Structured version   Visualization version   GIF version

Theorem sbcbiiOLD 38567
Description: Formula-building inference rule for class substitution. (Contributed by NM, 11-Nov-2005.) Obsolete as of 17-Aug-2018. Use sbcbii 3489 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Hypothesis
Ref Expression
sbcbiiOLD.1 (𝜑𝜓)
Assertion
Ref Expression
sbcbiiOLD (𝐴𝑉 → ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓))

Proof of Theorem sbcbiiOLD
StepHypRef Expression
1 sbcbiiOLD.1 . . 3 (𝜑𝜓)
21sbcbii 3489 . 2 ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓)
32a1i 11 1 (𝐴𝑉 → ([𝐴 / 𝑥]𝜑[𝐴 / 𝑥]𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 196  wcel 1989  [wsbc 3433
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1721  ax-4 1736  ax-5 1838  ax-6 1887  ax-7 1934  ax-9 1998  ax-10 2018  ax-11 2033  ax-12 2046  ax-13 2245  ax-ext 2601
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1485  df-ex 1704  df-nf 1709  df-sb 1880  df-clab 2608  df-cleq 2614  df-clel 2617  df-sbc 3434
This theorem is referenced by:  sbc3orgOLD  38568  sbcssOLD  38582  eqsbc3rVD  38901
  Copyright terms: Public domain W3C validator