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Mirrors > Home > ILE Home > Th. List > brab1 | Unicode version |
Description: Relationship between a binary relation and a class abstraction. (Contributed by Andrew Salmon, 8-Jul-2011.) |
Ref | Expression |
---|---|
brab1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 2724 | . . 3 | |
2 | breq1 3979 | . . . 4 | |
3 | breq1 3979 | . . . 4 | |
4 | 2, 3 | sbcie2g 2979 | . . 3 |
5 | 1, 4 | ax-mp 5 | . 2 |
6 | df-sbc 2947 | . 2 | |
7 | 5, 6 | bitr3i 185 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wcel 2135 cab 2150 cvv 2721 wsbc 2946 class class class wbr 3976 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-sbc 2947 df-un 3115 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 |
This theorem is referenced by: (None) |
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