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Mirrors > Home > ILE Home > Th. List > sbc5 | Unicode version |
Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
sbc5 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 2890 | . 2 | |
2 | exsimpl 1581 | . . 3 | |
3 | isset 2666 | . . 3 | |
4 | 2, 3 | sylibr 133 | . 2 |
5 | dfsbcq2 2885 | . . 3 | |
6 | eqeq2 2127 | . . . . 5 | |
7 | 6 | anbi1d 460 | . . . 4 |
8 | 7 | exbidv 1781 | . . 3 |
9 | sb5 1843 | . . 3 | |
10 | 5, 8, 9 | vtoclbg 2721 | . 2 |
11 | 1, 4, 10 | pm5.21nii 678 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 wsb 1720 cvv 2660 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: sbc6g 2906 sbc7 2908 sbciegft 2911 sbccomlem 2955 csb2 2977 rexsns 3533 |
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