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Mirrors > Home > NFE Home > Th. List > dvelimdf | Unicode version |
Description: Deduction form of dvelimf 1997. This version may be useful if we want to avoid ax-17 1616 and use ax-16 2144 instead. (Contributed by NM, 7-Apr-2004.) (Revised by Mario Carneiro, 6-Oct-2016.) |
Ref | Expression |
---|---|
dvelimdf.1 | |
dvelimdf.2 | |
dvelimdf.3 | |
dvelimdf.4 | |
dvelimdf.5 |
Ref | Expression |
---|---|
dvelimdf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dvelimdf.2 | . . . . . 6 | |
2 | dvelimdf.3 | . . . . . 6 | |
3 | 1, 2 | alrimi 1765 | . . . . 5 |
4 | nfsb4t 2080 | . . . . 5 | |
5 | 3, 4 | syl 15 | . . . 4 |
6 | 5 | imp 418 | . . 3 |
7 | dvelimdf.1 | . . . . 5 | |
8 | nfnae 1956 | . . . . 5 | |
9 | 7, 8 | nfan 1824 | . . . 4 |
10 | dvelimdf.4 | . . . . . 6 | |
11 | dvelimdf.5 | . . . . . 6 | |
12 | 1, 10, 11 | sbied 2036 | . . . . 5 |
13 | 12 | adantr 451 | . . . 4 |
14 | 9, 13 | nfbidf 1774 | . . 3 |
15 | 6, 14 | mpbid 201 | . 2 |
16 | 15 | ex 423 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wa 358 wal 1540 wnf 1544 wsb 1648 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 |
This theorem is referenced by: dvelimdc 2509 |
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