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Theorem sbcrel 5094
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 sbcssg 3940 . . 3
2 csbconstg 3447 . . . 4
32sseq2d 3531 . . 3
41, 3bitrd 253 . 2
5 df-rel 5011 . . 3
65sbcbii 3387 . 2
7 df-rel 5011 . 2
84, 6, 73bitr4g 288 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  e.wcel 1818   cvv 3109  [.wsbc 3327  [_csb 3434  C_wss 3475  X.cxp 5002  Relwrel 5009
This theorem is referenced by:  sbcfung  5616
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785  df-rel 5011
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