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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 2033 |
. 2
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2 | nfv 1418 |
. . 3
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3 | nfcvd 2176 |
. . . . 5
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4 | nfeqd.1 |
. . . . 5
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5 | 3, 4 | nfeqd 2189 |
. . . 4
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6 | nfeqd.2 |
. . . . 5
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7 | 6 | nfcrd 2188 |
. . . 4
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8 | 5, 7 | nfand 1457 |
. . 3
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9 | 2, 8 | nfexd 1641 |
. 2
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10 | 1, 9 | nfxfrd 1361 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-cleq 2030 df-clel 2033 df-nfc 2164 |
This theorem is referenced by: nfneld 2299 nfraldxy 2350 nfrexdxy 2351 nfreudxy 2477 nfsbc1d 2774 nfsbcd 2777 nfbrd 3798 nfriotadxy 5419 |
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