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

Theorem sbcang 3089
 Description: Distribution of class substitution over conjunction. (Contributed by NM, 21-May-2004.)
Assertion
Ref Expression
sbcang

Proof of Theorem sbcang
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3049 . 2
2 dfsbcq2 3049 . . 3
3 dfsbcq2 3049 . . 3
42, 3anbi12d 691 . 2
5 sban 2069 . 2
61, 4, 5vtoclbg 2915 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642  wsb 1648   wcel 1710  wsbc 3046 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-or 359  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-nfc 2478  df-v 2861  df-sbc 3047 This theorem is referenced by:  sbcabel  3123  csbunig  3899  csbxpg  4813
 Copyright terms: Public domain W3C validator