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Mirrors > Home > ILE Home > Th. List > sbc6g | Unicode version |
Description: An equivalence for class substitution. (Contributed by NM, 11-Oct-2004.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
sbc6g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1457 | . . 3 | |
2 | ceqex 2786 | . . 3 | |
3 | 1, 2 | ceqsalg 2688 | . 2 |
4 | sbc5 2905 | . 2 | |
5 | 3, 4 | syl6rbbr 198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wceq 1316 wex 1453 wcel 1465 wsbc 2882 |
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 |
This theorem is referenced by: sbc6 2907 sbciegft 2911 ralsnsg 3531 ralsns 3532 fz1sbc 9844 |
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