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Mirrors > Home > MPE Home > Th. List > eeeanv | Structured version Visualization version Unicode version |
Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.) (Proof shortened by Andrew Salmon, 25-May-2011.) Reduce distinct variable restrictions. (Revised by Wolf Lammen, 20-Jan-2018.) |
Ref | Expression |
---|---|
eeeanv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eeanv 2182 | . . 3 | |
2 | 1 | anbi1i 731 | . 2 |
3 | df-3an 1039 | . . . . . 6 | |
4 | 3 | exbii 1774 | . . . . 5 |
5 | 19.42v 1918 | . . . . 5 | |
6 | 4, 5 | bitri 264 | . . . 4 |
7 | 6 | 2exbii 1775 | . . 3 |
8 | nfv 1843 | . . . . . 6 | |
9 | 8 | nfex 2154 | . . . . 5 |
10 | 9 | 19.41 2103 | . . . 4 |
11 | 10 | exbii 1774 | . . 3 |
12 | nfv 1843 | . . . . 5 | |
13 | 12 | nfex 2154 | . . . 4 |
14 | 13 | 19.41 2103 | . . 3 |
15 | 7, 11, 14 | 3bitri 286 | . 2 |
16 | df-3an 1039 | . 2 | |
17 | 2, 15, 16 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 w3a 1037 wex 1704 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-ex 1705 df-nf 1710 |
This theorem is referenced by: vtocl3 3262 spc3egv 3297 eloprabga 6747 |
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