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Theorem sbcrel 4593
 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 3440 . . 3
2 csbconstg 2985 . . . 4
32sseq2d 3095 . . 3
41, 3bitrd 187 . 2
5 df-rel 4514 . . 3
65sbcbii 2938 . 2
7 df-rel 4514 . 2
84, 6, 73bitr4g 222 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wcel 1463  cvv 2658  wsbc 2880  csb 2973   wss 3039   cxp 4505   wrel 4512 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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-sbc 2881  df-csb 2974  df-in 3045  df-ss 3052  df-rel 4514 This theorem is referenced by:  sbcfung  5115
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