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Mirrors > Home > ILE Home > Th. List > ax11v | Unicode version |
Description: This is a version of ax-11o 1704 when the variables are distinct. Axiom (C8) of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.) (Revised by Jim Kingdon, 15-Dec-2017.) |
Ref | Expression |
---|---|
ax11v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1586 | . 2 | |
2 | ax-17 1419 | . . . . 5 | |
3 | ax-11 1397 | . . . . 5 | |
4 | 2, 3 | syl5 28 | . . . 4 |
5 | equequ2 1599 | . . . . 5 | |
6 | 5 | imbi1d 220 | . . . . . . 7 |
7 | 6 | albidv 1705 | . . . . . 6 |
8 | 7 | imbi2d 219 | . . . . 5 |
9 | 5, 8 | imbi12d 223 | . . . 4 |
10 | 4, 9 | mpbii 136 | . . 3 |
11 | 10 | exlimiv 1489 | . 2 |
12 | 1, 11 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1241 wceq 1243 wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-ie2 1383 ax-8 1395 ax-11 1397 ax-17 1419 ax-i9 1423 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: equs5or 1711 sb56 1765 |
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