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Mirrors > Home > MPE Home > Th. List > reuxfr2d | Structured version Visualization version Unicode version |
Description: Transfer existential uniqueness from a variable to another variable contained in expression . (Contributed by NM, 16-Jan-2012.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
reuxfr2d.1 | |
reuxfr2d.2 |
Ref | Expression |
---|---|
reuxfr2d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reuxfr2d.2 | . . . . . . 7 | |
2 | rmoan 3406 | . . . . . . 7 | |
3 | 1, 2 | syl 17 | . . . . . 6 |
4 | ancom 466 | . . . . . . 7 | |
5 | 4 | rmobii 3133 | . . . . . 6 |
6 | 3, 5 | sylib 208 | . . . . 5 |
7 | 6 | ralrimiva 2966 | . . . 4 |
8 | 2reuswap 3410 | . . . 4 | |
9 | 7, 8 | syl 17 | . . 3 |
10 | df-rmo 2920 | . . . . . 6 | |
11 | 10 | ralbii 2980 | . . . . 5 |
12 | 2reuswap 3410 | . . . . 5 | |
13 | 11, 12 | sylbir 225 | . . . 4 |
14 | moeq 3382 | . . . . . . 7 | |
15 | 14 | moani 2525 | . . . . . 6 |
16 | ancom 466 | . . . . . . . 8 | |
17 | an12 838 | . . . . . . . 8 | |
18 | 16, 17 | bitri 264 | . . . . . . 7 |
19 | 18 | mobii 2493 | . . . . . 6 |
20 | 15, 19 | mpbi 220 | . . . . 5 |
21 | 20 | a1i 11 | . . . 4 |
22 | 13, 21 | mprg 2926 | . . 3 |
23 | 9, 22 | impbid1 215 | . 2 |
24 | reuxfr2d.1 | . . . 4 | |
25 | biidd 252 | . . . . 5 | |
26 | 25 | ceqsrexv 3336 | . . . 4 |
27 | 24, 26 | syl 17 | . . 3 |
28 | 27 | reubidva 3125 | . 2 |
29 | 23, 28 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wmo 2471 wral 2912 wrex 2913 wreu 2914 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-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-v 3202 |
This theorem is referenced by: reuxfr2 4892 reuxfrd 4893 |
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