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Mirrors > Home > ILE Home > Th. List > ax11ev | Unicode version |
Description: Analogue to ax11v 1807 for existential quantification. (Contributed by Jim Kingdon, 9-Jan-2018.) |
Ref | Expression |
---|---|
ax11ev |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1676 | . 2 | |
2 | ax11e 1776 | . . . . 5 | |
3 | ax-17 1506 | . . . . . 6 | |
4 | 3 | 19.9h 1623 | . . . . 5 |
5 | 2, 4 | syl6ib 160 | . . . 4 |
6 | equequ2 1693 | . . . . 5 | |
7 | 6 | anbi1d 461 | . . . . . . 7 |
8 | 7 | exbidv 1805 | . . . . . 6 |
9 | 8 | imbi1d 230 | . . . . 5 |
10 | 6, 9 | imbi12d 233 | . . . 4 |
11 | 5, 10 | mpbii 147 | . . 3 |
12 | 11 | exlimiv 1578 | . 2 |
13 | 1, 12 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1335 wex 1472 |
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-5 1427 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: (None) |
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