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Mirrors > Home > NFE Home > Th. List > nfceqi | Unicode version |
Description: Equality theorem for class not-free. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfceqi.1 |
Ref | Expression |
---|---|
nfceqi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfceqi.1 | . . . . 5 | |
2 | 1 | eleq2i 2417 | . . . 4 |
3 | 2 | nfbii 1569 | . . 3 |
4 | 3 | albii 1566 | . 2 |
5 | df-nfc 2478 | . 2 | |
6 | df-nfc 2478 | . 2 | |
7 | 4, 5, 6 | 3bitr4i 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 176 wal 1540 wnf 1544 wceq 1642 wcel 1710 wnfc 2476 |
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-cleq 2346 df-clel 2349 df-nfc 2478 |
This theorem is referenced by: nfcxfr 2486 nfcxfrd 2487 |
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