Mathbox for Wolf Lammen |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > wl-ax13lem1 | Structured version Visualization version Unicode version |
Description: A version of ax-wl-13v 33286 with one distinct variable restriction dropped. For convenience, is kept on the right side of equations. This proof bases on ideas from NM, 24-Dec-2015. (Contributed by Wolf Lammen, 23-Jul-2021.) |
Ref | Expression |
---|---|
wl-ax13lem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equviniva 1960 | . 2 | |
2 | ax-wl-13v 33286 | . . . . 5 | |
3 | equeucl 1951 | . . . . . 6 | |
4 | 3 | alimdv 1845 | . . . . 5 |
5 | 2, 4 | syl9 77 | . . . 4 |
6 | 5 | impd 447 | . . 3 |
7 | 6 | exlimdv 1861 | . 2 |
8 | 1, 7 | syl5 34 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wa 384 wal 1481 wex 1704 |
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-wl-13v 33286 |
This theorem depends on definitions: df-bi 197 df-an 386 df-ex 1705 |
This theorem is referenced by: (None) |
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