Mathbox for Alexander van der Vekens < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  sbcrel Unicode version

Theorem sbcrel 27651
 Description: Distribute proper substitution through a relation predicate. (Contributed by Alexander van der Vekens, 23-Jul-2017.)
Assertion
Ref Expression
sbcrel

Proof of Theorem sbcrel
StepHypRef Expression
1 sbcss 3683 . . 3
2 csbconstg 3210 . . . 4
32sseq2d 3321 . . 3
41, 3bitrd 245 . 2
5 df-rel 4827 . . 3
65sbcbii 3161 . 2
7 df-rel 4827 . 2
84, 6, 73bitr4g 280 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wcel 1717  cvv 2901  wsbc 3106  csb 3196   wss 3265   cxp 4818   wrel 4825 This theorem is referenced by:  sbcfun  27657 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-v 2903  df-sbc 3107  df-csb 3197  df-in 3272  df-ss 3279  df-rel 4827
 Copyright terms: Public domain W3C validator