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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 1293 |
. . . 4
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2 | csbeq1a 2941 |
. . . . . . 7
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3 | 2 | equcoms 1641 |
. . . . . 6
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4 | a1tru 1305 |
. . . . . 6
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5 | 3, 4 | 2thd 173 |
. . . . 5
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6 | 5 | rspcev 2722 |
. . . 4
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7 | 1, 6 | mpan2 416 |
. . 3
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8 | elabrex.1 |
. . . 4
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9 | eqeq1 2094 |
. . . . 5
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10 | 9 | rexbidv 2381 |
. . . 4
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11 | 8, 10 | elab 2760 |
. . 3
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12 | 7, 11 | sylibr 132 |
. 2
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13 | nfv 1466 |
. . . 4
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14 | nfcsb1v 2963 |
. . . . 5
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15 | 14 | nfeq2 2240 |
. . . 4
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16 | 2 | eqeq2d 2099 |
. . . 4
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17 | 13, 15, 16 | cbvrex 2587 |
. . 3
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18 | 17 | abbii 2203 |
. 2
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19 | 12, 18 | syl6eleqr 2181 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rex 2365 df-v 2621 df-sbc 2841 df-csb 2934 |
This theorem is referenced by: eusvobj2 5638 |
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