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Mirrors > Home > ILE Home > Th. List > nfrexdxy | Unicode version |
Description: Not-free for restricted existential quantification where and are distinct. See nfrexdya 2359 for a version with and distinct instead. (Contributed by Jim Kingdon, 30-May-2018.) |
Ref | Expression |
---|---|
nfraldxy.2 | |
nfraldxy.3 | |
nfraldxy.4 |
Ref | Expression |
---|---|
nfrexdxy |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2312 | . 2 | |
2 | nfraldxy.2 | . . 3 | |
3 | nfcv 2178 | . . . . . 6 | |
4 | 3 | a1i 9 | . . . . 5 |
5 | nfraldxy.3 | . . . . 5 | |
6 | 4, 5 | nfeld 2193 | . . . 4 |
7 | nfraldxy.4 | . . . 4 | |
8 | 6, 7 | nfand 1460 | . . 3 |
9 | 2, 8 | nfexd 1644 | . 2 |
10 | 1, 9 | nfxfrd 1364 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wnf 1349 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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rex 2312 |
This theorem is referenced by: nfrexdya 2359 nfrexxy 2361 nfunid 3587 strcollnft 10109 |
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