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Mirrors > Home > ILE Home > Th. List > nfeld | Unicode version |
Description: Hypothesis builder for elementhood. (Contributed by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
nfeqd.1 |
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nfeqd.2 |
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Ref | Expression |
---|---|
nfeld |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-clel 2136 |
. 2
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2 | nfv 1509 |
. . 3
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3 | nfcvd 2283 |
. . . . 5
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4 | nfeqd.1 |
. . . . 5
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5 | 3, 4 | nfeqd 2297 |
. . . 4
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6 | nfeqd.2 |
. . . . 5
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7 | 6 | nfcrd 2296 |
. . . 4
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8 | 5, 7 | nfand 1548 |
. . 3
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9 | 2, 8 | nfexd 1735 |
. 2
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10 | 1, 9 | nfxfrd 1452 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-cleq 2133 df-clel 2136 df-nfc 2271 |
This theorem is referenced by: nfneld 2412 nfraldxy 2470 nfrexdxy 2471 nfreudxy 2607 nfsbc1d 2929 nfsbcd 2932 sbcrext 2990 nfbrd 3981 nfriotadxy 5746 nfixpxy 6619 |
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