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Mirrors > Home > ILE Home > Th. List > nfceqdf | Unicode version |
Description: An equality theorem for effectively not free. (Contributed by Mario Carneiro, 14-Oct-2016.) |
Ref | Expression |
---|---|
nfceqdf.1 |
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nfceqdf.2 |
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Ref | Expression |
---|---|
nfceqdf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfceqdf.1 |
. . . 4
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2 | nfceqdf.2 |
. . . . 5
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3 | 2 | eleq2d 2184 |
. . . 4
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4 | 1, 3 | nfbidf 1502 |
. . 3
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5 | 4 | albidv 1778 |
. 2
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6 | df-nfc 2244 |
. 2
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7 | df-nfc 2244 |
. 2
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8 | 5, 6, 7 | 3bitr4g 222 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-4 1470 ax-17 1489 ax-ial 1497 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-cleq 2108 df-clel 2111 df-nfc 2244 |
This theorem is referenced by: nfopd 3688 dfnfc2 3720 nfimad 4848 nffvd 5387 |
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