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Mirrors > Home > MPE Home > Th. List > reean | Structured version Visualization version Unicode version |
Description: Rearrange restricted existential quantifiers. (Contributed by NM, 27-Oct-2010.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
reean.1 | |
reean.2 |
Ref | Expression |
---|---|
reean |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an4 865 | . . . 4 | |
2 | 1 | 2exbii 1775 | . . 3 |
3 | nfv 1843 | . . . . 5 | |
4 | reean.1 | . . . . 5 | |
5 | 3, 4 | nfan 1828 | . . . 4 |
6 | nfv 1843 | . . . . 5 | |
7 | reean.2 | . . . . 5 | |
8 | 6, 7 | nfan 1828 | . . . 4 |
9 | 5, 8 | eean 2181 | . . 3 |
10 | 2, 9 | bitri 264 | . 2 |
11 | r2ex 3061 | . 2 | |
12 | df-rex 2918 | . . 3 | |
13 | df-rex 2918 | . . 3 | |
14 | 12, 13 | anbi12i 733 | . 2 |
15 | 10, 11, 14 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wnf 1708 wcel 1990 wrex 2913 |
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-tru 1486 df-ex 1705 df-nf 1710 df-ral 2917 df-rex 2918 |
This theorem is referenced by: reeanv 3107 disjrnmpt2 39375 |
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