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Mirrors > Home > ILE Home > Th. List > ax11v | Unicode version |
Description: This is a version of ax-11o 1744 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 1626 | . 2 | |
2 | ax-17 1459 | . . . . 5 | |
3 | ax-11 1437 | . . . . 5 | |
4 | 2, 3 | syl5 32 | . . . 4 |
5 | equequ2 1639 | . . . . 5 | |
6 | 5 | imbi1d 229 | . . . . . . 7 |
7 | 6 | albidv 1745 | . . . . . 6 |
8 | 7 | imbi2d 228 | . . . . 5 |
9 | 5, 8 | imbi12d 232 | . . . 4 |
10 | 4, 9 | mpbii 146 | . . 3 |
11 | 10 | exlimiv 1529 | . 2 |
12 | 1, 11 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1282 wceq 1284 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-gen 1378 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-17 1459 ax-i9 1463 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: equs5or 1751 sb56 1806 |
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