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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 | sbc5 2969 | . 2 | |
2 | nfe1 1483 | . . 3 | |
3 | ceqex 2848 | . . 3 | |
4 | 2, 3 | ceqsalg 2749 | . 2 |
5 | 1, 4 | bitr4id 198 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wceq 1342 wex 1479 wcel 2135 wsbc 2946 |
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-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 |
This theorem is referenced by: sbc6 2971 sbciegft 2976 ralsnsg 3607 ralsns 3608 fz1sbc 10021 |
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