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Mirrors > Home > ILE Home > Th. List > csbrng | Unicode version |
Description: Distribute proper substitution through the range of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbrng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabg 3056 | . . 3 | |
2 | sbcexg 2958 | . . . . 5 | |
3 | sbcel2g 3018 | . . . . . 6 | |
4 | 3 | exbidv 1797 | . . . . 5 |
5 | 2, 4 | bitrd 187 | . . . 4 |
6 | 5 | abbidv 2255 | . . 3 |
7 | 1, 6 | eqtrd 2170 | . 2 |
8 | dfrn3 4723 | . . 3 | |
9 | 8 | csbeq2i 3024 | . 2 |
10 | dfrn3 4723 | . 2 | |
11 | 7, 9, 10 | 3eqtr4g 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wex 1468 wcel 1480 cab 2123 wsbc 2904 csb 2998 cop 3525 crn 4535 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-br 3925 df-opab 3985 df-cnv 4542 df-dm 4544 df-rn 4545 |
This theorem is referenced by: sbcfg 5266 |
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