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Mirrors > Home > ILE Home > Th. List > elabrex | Unicode version |
Description: Elementhood in an image set. (Contributed by Mario Carneiro, 14-Jan-2014.) |
Ref | Expression |
---|---|
elabrex.1 |
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Ref | Expression |
---|---|
elabrex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1368 |
. . . 4
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2 | csbeq1a 3081 |
. . . . . . 7
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3 | 2 | equcoms 1719 |
. . . . . 6
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4 | trud 1380 |
. . . . . 6
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5 | 3, 4 | 2thd 175 |
. . . . 5
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6 | 5 | rspcev 2856 |
. . . 4
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7 | 1, 6 | mpan2 425 |
. . 3
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8 | elabrex.1 |
. . . 4
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9 | eqeq1 2196 |
. . . . 5
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10 | 9 | rexbidv 2491 |
. . . 4
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11 | 8, 10 | elab 2896 |
. . 3
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12 | 7, 11 | sylibr 134 |
. 2
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13 | nfv 1539 |
. . . 4
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14 | nfcsb1v 3105 |
. . . . 5
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15 | 14 | nfeq2 2344 |
. . . 4
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16 | 2 | eqeq2d 2201 |
. . . 4
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17 | 13, 15, 16 | cbvrex 2715 |
. . 3
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18 | 17 | abbii 2305 |
. 2
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19 | 12, 18 | eleqtrrdi 2283 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-sbc 2978 df-csb 3073 |
This theorem is referenced by: eusvobj2 5883 |
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