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Theorem sbc3an 3313
 Description: Distribution of class substitution over triple conjunction. (Contributed by NM, 14-Dec-2006.) (Revised by NM, 17-Aug-2018.)
Assertion
Ref Expression
sbc3an

Proof of Theorem sbc3an
StepHypRef Expression
1 df-3an 1009 . . . 4
21sbcbii 3311 . . 3
3 sbcan 3298 . . 3
4 sbcan 3298 . . . 4
54anbi1i 709 . . 3
62, 3, 53bitri 279 . 2
7 df-3an 1009 . 2
86, 7bitr4i 260 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   w3a 1007  wsbc 3255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-v 3033  df-sbc 3256 This theorem is referenced by:  bnj156  29608  bnj206  29611  bnj976  29661  bnj121  29753  bnj130  29757  bnj581  29791  bnj1040  29853  csbwrecsg  31798  topdifinffinlem  31820  rdgeqoa  31843  cdlemkid3N  34571  cdlemkid4  34572
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