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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 2917 | . 2 | |
2 | exsimpl 1596 | . . 3 | |
3 | isset 2692 | . . 3 | |
4 | 2, 3 | sylibr 133 | . 2 |
5 | dfsbcq2 2912 | . . 3 | |
6 | eqeq2 2149 | . . . . 5 | |
7 | 6 | anbi1d 460 | . . . 4 |
8 | 7 | exbidv 1797 | . . 3 |
9 | sb5 1859 | . . 3 | |
10 | 5, 8, 9 | vtoclbg 2747 | . 2 |
11 | 1, 4, 10 | pm5.21nii 693 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 wsb 1735 cvv 2686 wsbc 2909 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sbc 2910 |
This theorem is referenced by: sbc6g 2933 sbc7 2935 sbciegft 2939 sbccomlem 2983 csb2 3005 rexsns 3563 |
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