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Mirrors > Home > MPE Home > Th. List > nfceqi | Structured version Visualization version Unicode version |
Description: Equality theorem for class not-free. (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) |
Ref | Expression |
---|---|
nfceqi.1 |
Ref | Expression |
---|---|
nfceqi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1730 | . . 3 | |
2 | nfceqi.1 | . . . 4 | |
3 | 2 | a1i 11 | . . 3 |
4 | 1, 3 | nfceqdf 2760 | . 2 |
5 | 4 | trud 1493 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wtru 1484 wnfc 2751 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-12 2047 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-cleq 2615 df-clel 2618 df-nfc 2753 |
This theorem is referenced by: nfcxfr 2762 nfcxfrd 2763 |
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