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Mirrors > Home > ILE Home > Th. List > sbcrel | Unicode version |
Description: Distribute proper substitution through a relation predicate. (Contributed by Alexander van der Vekens, 23-Jul-2017.) |
Ref | Expression |
---|---|
sbcrel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcssg 3442 | . . 3 | |
2 | csbconstg 2987 | . . . 4 | |
3 | 2 | sseq2d 3097 | . . 3 |
4 | 1, 3 | bitrd 187 | . 2 |
5 | df-rel 4516 | . . 3 | |
6 | 5 | sbcbii 2940 | . 2 |
7 | df-rel 4516 | . 2 | |
8 | 4, 6, 7 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 1465 cvv 2660 wsbc 2882 csb 2975 wss 3041 cxp 4507 wrel 4514 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sbc 2883 df-csb 2976 df-in 3047 df-ss 3054 df-rel 4516 |
This theorem is referenced by: sbcfung 5117 |
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