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Mirrors > Home > MPE Home > Th. List > nfald | Structured version Visualization version Unicode version |
Description: Deduction form of nfal 2153. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 6-Jan-2018.) (Proof shortened by Wolf Lammen, 16-Oct-2021.) |
Ref | Expression |
---|---|
nfald.1 | |
nfald.2 |
Ref | Expression |
---|---|
nfald |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.12 2164 | . . 3 | |
2 | nfald.1 | . . . 4 | |
3 | nfald.2 | . . . . 5 | |
4 | 3 | nfrd 1717 | . . . 4 |
5 | 2, 4 | alimd 2081 | . . 3 |
6 | ax-11 2034 | . . 3 | |
7 | 1, 5, 6 | syl56 36 | . 2 |
8 | 7 | nfd 1716 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1481 wex 1704 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-11 2034 ax-12 2047 |
This theorem depends on definitions: df-bi 197 df-or 385 df-ex 1705 df-nf 1710 |
This theorem is referenced by: nfexd 2167 dvelimhw 2173 nfald2 2331 nfeqd 2772 axrepndlem1 9414 axrepndlem2 9415 axunnd 9418 axpowndlem2 9420 axpowndlem4 9422 axregndlem2 9425 axinfndlem1 9427 axinfnd 9428 axacndlem4 9432 axacndlem5 9433 axacnd 9434 bj-dvelimdv 32834 wl-mo2df 33352 wl-eudf 33354 wl-mo2t 33357 nfintd 42420 |
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