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Mirrors > Home > ILE Home > Th. List > elsb4 | Unicode version |
Description: Substitution applied to an atomic membership wff. (Contributed by Rodolfo Medina, 3-Apr-2010.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) |
Ref | Expression |
---|---|
elsb4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1513 | . . . . 5 | |
2 | elequ2 2140 | . . . . 5 | |
3 | 1, 2 | sbieh 1777 | . . . 4 |
4 | 3 | sbbii 1752 | . . 3 |
5 | ax-17 1513 | . . . 4 | |
6 | 5 | sbco2h 1951 | . . 3 |
7 | 4, 6 | bitr3i 185 | . 2 |
8 | equsb1 1772 | . . . 4 | |
9 | elequ2 2140 | . . . . 5 | |
10 | 9 | sbimi 1751 | . . . 4 |
11 | 8, 10 | ax-mp 5 | . . 3 |
12 | sbbi 1946 | . . 3 | |
13 | 11, 12 | mpbi 144 | . 2 |
14 | ax-17 1513 | . . 3 | |
15 | 14 | sbh 1763 | . 2 |
16 | 7, 13, 15 | 3bitri 205 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wsb 1749 |
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-14 2138 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 |
This theorem is referenced by: (None) |
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