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Mirrors > Home > MPE Home > Th. List > reusv2lem2OLD | Structured version Visualization version Unicode version |
Description: Obsolete proof of reusv2lem2 4869 as of 7-Aug-2021. (Contributed by NM, 27-Oct-2010.) (Proof shortened by Mario Carneiro, 19-Nov-2016.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
reusv2lem2OLD |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eunex 4859 | . . . . 5 | |
2 | exnal 1754 | . . . . 5 | |
3 | 1, 2 | sylib 208 | . . . 4 |
4 | rzal 4073 | . . . . 5 | |
5 | 4 | alrimiv 1855 | . . . 4 |
6 | 3, 5 | nsyl3 133 | . . 3 |
7 | 6 | pm2.21d 118 | . 2 |
8 | simpr 477 | . . . 4 | |
9 | euex 2494 | . . . . . . 7 | |
10 | eqeq1 2626 | . . . . . . . . 9 | |
11 | 10 | ralbidv 2986 | . . . . . . . 8 |
12 | 11 | cbvexv 2275 | . . . . . . 7 |
13 | 9, 12 | sylib 208 | . . . . . 6 |
14 | nfv 1843 | . . . . . . . . . . . 12 | |
15 | nfra1 2941 | . . . . . . . . . . . 12 | |
16 | 14, 15 | nfan 1828 | . . . . . . . . . . 11 |
17 | nfra1 2941 | . . . . . . . . . . 11 | |
18 | simprr 796 | . . . . . . . . . . . . . 14 | |
19 | rspa 2930 | . . . . . . . . . . . . . . 15 | |
20 | 19 | ad2ant2lr 784 | . . . . . . . . . . . . . 14 |
21 | 18, 20 | eqtr4d 2659 | . . . . . . . . . . . . 13 |
22 | simplr 792 | . . . . . . . . . . . . . 14 | |
23 | 22, 11 | syl5ibrcom 237 | . . . . . . . . . . . . 13 |
24 | 21, 23 | mpd 15 | . . . . . . . . . . . 12 |
25 | 24 | exp32 631 | . . . . . . . . . . 11 |
26 | 16, 17, 25 | rexlimd 3026 | . . . . . . . . . 10 |
27 | r19.2z 4060 | . . . . . . . . . . . 12 | |
28 | 27 | ex 450 | . . . . . . . . . . 11 |
29 | 28 | adantr 481 | . . . . . . . . . 10 |
30 | 26, 29 | impbid 202 | . . . . . . . . 9 |
31 | 30 | eubidv 2490 | . . . . . . . 8 |
32 | 31 | ex 450 | . . . . . . 7 |
33 | 32 | exlimdv 1861 | . . . . . 6 |
34 | 13, 33 | syl5 34 | . . . . 5 |
35 | 34 | imp 445 | . . . 4 |
36 | 8, 35 | mpbird 247 | . . 3 |
37 | 36 | ex 450 | . 2 |
38 | 7, 37 | pm2.61ine 2877 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wal 1481 wceq 1483 wex 1704 wcel 1990 weu 2470 wne 2794 wral 2912 wrex 2913 c0 3915 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-nul 4789 ax-pow 4843 |
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-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-v 3202 df-dif 3577 df-nul 3916 |
This theorem is referenced by: (None) |
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