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Mirrors > Home > ILE Home > Th. List > r2exf | Unicode version |
Description: Double restricted existential quantification. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
r2alf.1 |
Ref | Expression |
---|---|
r2exf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . 2 | |
2 | r2alf.1 | . . . . . 6 | |
3 | 2 | nfcri 2172 | . . . . 5 |
4 | 3 | 19.42 1578 | . . . 4 |
5 | anass 381 | . . . . 5 | |
6 | 5 | exbii 1496 | . . . 4 |
7 | df-rex 2312 | . . . . 5 | |
8 | 7 | anbi2i 430 | . . . 4 |
9 | 4, 6, 8 | 3bitr4i 201 | . . 3 |
10 | 9 | exbii 1496 | . 2 |
11 | 1, 10 | bitr4i 176 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wex 1381 wcel 1393 wnfc 2165 wrex 2307 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 |
This theorem is referenced by: r2ex 2344 rexcomf 2472 |
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