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Mirrors > Home > MPE Home > Th. List > Mathboxes > 2rmoswap | Structured version Visualization version Unicode version |
Description: A condition allowing swap of restricted "at most one" and restricted existential quantifiers, analogous to 2moswap 2547. (Contributed by Alexander van der Vekens, 25-Jun-2017.) |
Ref | Expression |
---|---|
2rmoswap |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2920 | . . 3 | |
2 | 1 | ralbii 2980 | . 2 |
3 | df-ral 2917 | . . . 4 | |
4 | moanimv 2531 | . . . . 5 | |
5 | 4 | albii 1747 | . . . 4 |
6 | 3, 5 | bitr4i 267 | . . 3 |
7 | 2moswap 2547 | . . . 4 | |
8 | df-rmo 2920 | . . . . 5 | |
9 | r19.42v 3092 | . . . . . . 7 | |
10 | df-rex 2918 | . . . . . . . 8 | |
11 | an12 838 | . . . . . . . . 9 | |
12 | 11 | exbii 1774 | . . . . . . . 8 |
13 | 10, 12 | bitri 264 | . . . . . . 7 |
14 | 9, 13 | bitr3i 266 | . . . . . 6 |
15 | 14 | mobii 2493 | . . . . 5 |
16 | 8, 15 | bitri 264 | . . . 4 |
17 | df-rmo 2920 | . . . . 5 | |
18 | r19.42v 3092 | . . . . . . 7 | |
19 | df-rex 2918 | . . . . . . 7 | |
20 | 18, 19 | bitr3i 266 | . . . . . 6 |
21 | 20 | mobii 2493 | . . . . 5 |
22 | 17, 21 | bitri 264 | . . . 4 |
23 | 7, 16, 22 | 3imtr4g 285 | . . 3 |
24 | 6, 23 | sylbi 207 | . 2 |
25 | 2, 24 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wal 1481 wex 1704 wcel 1990 wmo 2471 wral 2912 wrex 2913 wrmo 2915 |
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 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 df-ral 2917 df-rex 2918 df-rmo 2920 |
This theorem is referenced by: 2reu1 41186 |
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