Mathbox for Wolf Lammen |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-ax11-lem3 | Structured version Visualization version Unicode version |
Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019.) |
Ref | Expression |
---|---|
wl-ax11-lem3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfna1 2029 | . 2 | |
2 | wl-naev 33302 | . . . . 5 | |
3 | nfa1 2028 | . . . . . . 7 | |
4 | nfna1 2029 | . . . . . . 7 | |
5 | 3, 4 | nfan 1828 | . . . . . 6 |
6 | axc11n 2307 | . . . . . . . . . . 11 | |
7 | wl-aetr 33317 | . . . . . . . . . . 11 | |
8 | 6, 7 | syl5 34 | . . . . . . . . . 10 |
9 | 8 | aecoms 2312 | . . . . . . . . 9 |
10 | 9 | con3d 148 | . . . . . . . 8 |
11 | 10 | imdistani 726 | . . . . . . 7 |
12 | wl-ax11-lem2 33363 | . . . . . . 7 | |
13 | 11, 12 | syl 17 | . . . . . 6 |
14 | 5, 13 | alrimi 2082 | . . . . 5 |
15 | 2, 14 | sylan2 491 | . . . 4 |
16 | 15 | expcom 451 | . . 3 |
17 | ax-wl-11v 33361 | . . 3 | |
18 | 16, 17 | syl6 35 | . 2 |
19 | 1, 18 | nf5d 2118 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wal 1481 wnf 1708 |
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-12 2047 ax-13 2246 ax-wl-11v 33361 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 |
This theorem is referenced by: wl-ax11-lem4 33365 wl-ax11-lem6 33367 |
Copyright terms: Public domain | W3C validator |