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Theorem sbcrel 27971
 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 3740 . . 3
2 csbconstg 3267 . . . 4
32sseq2d 3378 . . 3
41, 3bitrd 246 . 2
5 df-rel 4888 . . 3
65sbcbii 3218 . 2
7 df-rel 4888 . 2
84, 6, 73bitr4g 281 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wcel 1726  cvv 2958  wsbc 3163  csb 3253   wss 3322   cxp 4879   wrel 4886 This theorem is referenced by:  sbcfun  27977 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-sbc 3164  df-csb 3254  df-in 3329  df-ss 3336  df-rel 4888
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