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Mirrors > Home > MPE Home > Th. List > rmo3 | Structured version Visualization version Unicode version |
Description: Restricted "at most one" using explicit substitution. (Contributed by NM, 4-Nov-2012.) (Revised by NM, 16-Jun-2017.) |
Ref | Expression |
---|---|
rmo2.1 |
Ref | Expression |
---|---|
rmo3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rmo 2920 | . 2 | |
2 | sban 2399 | . . . . . . . . . . 11 | |
3 | clelsb3 2729 | . . . . . . . . . . . 12 | |
4 | 3 | anbi1i 731 | . . . . . . . . . . 11 |
5 | 2, 4 | bitri 264 | . . . . . . . . . 10 |
6 | 5 | anbi2i 730 | . . . . . . . . 9 |
7 | an4 865 | . . . . . . . . 9 | |
8 | ancom 466 | . . . . . . . . . 10 | |
9 | 8 | anbi1i 731 | . . . . . . . . 9 |
10 | 6, 7, 9 | 3bitri 286 | . . . . . . . 8 |
11 | 10 | imbi1i 339 | . . . . . . 7 |
12 | impexp 462 | . . . . . . 7 | |
13 | impexp 462 | . . . . . . 7 | |
14 | 11, 12, 13 | 3bitri 286 | . . . . . 6 |
15 | 14 | albii 1747 | . . . . 5 |
16 | df-ral 2917 | . . . . 5 | |
17 | r19.21v 2960 | . . . . 5 | |
18 | 15, 16, 17 | 3bitr2i 288 | . . . 4 |
19 | 18 | albii 1747 | . . 3 |
20 | nfv 1843 | . . . . 5 | |
21 | rmo2.1 | . . . . 5 | |
22 | 20, 21 | nfan 1828 | . . . 4 |
23 | 22 | mo3 2507 | . . 3 |
24 | df-ral 2917 | . . 3 | |
25 | 19, 23, 24 | 3bitr4i 292 | . 2 |
26 | 1, 25 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wal 1481 wnf 1708 wsb 1880 wcel 1990 wmo 2471 wral 2912 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-cleq 2615 df-clel 2618 df-ral 2917 df-rmo 2920 |
This theorem is referenced by: poimirlem25 33434 poimirlem26 33435 |
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