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Mirrors > Home > NFE Home > Th. List > eqvinc | Unicode version |
Description: A variable introduction law for class equality. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 8-Jun-2011.) |
Ref | Expression |
---|---|
eqvinc.1 |
Ref | Expression |
---|---|
eqvinc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqvinc.1 | . . . . 5 | |
2 | 1 | isseti 2865 | . . . 4 |
3 | ax-1 6 | . . . . . 6 | |
4 | eqtr 2370 | . . . . . . 7 | |
5 | 4 | ex 423 | . . . . . 6 |
6 | 3, 5 | jca 518 | . . . . 5 |
7 | 6 | eximi 1576 | . . . 4 |
8 | pm3.43 832 | . . . . 5 | |
9 | 8 | eximi 1576 | . . . 4 |
10 | 2, 7, 9 | mp2b 9 | . . 3 |
11 | 10 | 19.37aiv 1900 | . 2 |
12 | eqtr2 2371 | . . 3 | |
13 | 12 | exlimiv 1634 | . 2 |
14 | 11, 13 | impbii 180 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wex 1541 wceq 1642 wcel 1710 cvv 2859 |
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-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-v 2861 |
This theorem is referenced by: eqvincf 2967 preaddccan2lem1 4454 dff13 5471 nncdiv3lem1 6275 |
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