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Mirrors > Home > ILE Home > Th. List > ax11ev | Unicode version |
Description: Analogue to ax11v 1748 for existential quantification. (Contributed by Jim Kingdon, 9-Jan-2018.) |
Ref | Expression |
---|---|
ax11ev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1626 | . 2 | |
2 | ax11e 1717 | . . . . 5 | |
3 | ax-17 1459 | . . . . . 6 | |
4 | 3 | 19.9h 1574 | . . . . 5 |
5 | 2, 4 | syl6ib 159 | . . . 4 |
6 | equequ2 1639 | . . . . 5 | |
7 | 6 | anbi1d 452 | . . . . . . 7 |
8 | 7 | exbidv 1746 | . . . . . 6 |
9 | 8 | imbi1d 229 | . . . . 5 |
10 | 6, 9 | imbi12d 232 | . . . 4 |
11 | 5, 10 | mpbii 146 | . . 3 |
12 | 11 | exlimiv 1529 | . 2 |
13 | 1, 12 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
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