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Theorem sbcang 2952
 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 2912 . 2
2 dfsbcq2 2912 . . 3
3 dfsbcq2 2912 . . 3
42, 3anbi12d 464 . 2
5 sban 1928 . 2
61, 4, 5vtoclbg 2747 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331   wcel 1480  wsb 1735  wsbc 2909 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-sbc 2910 This theorem is referenced by:  sbcabel  2990  csbunig  3747  csbxpg  4623
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