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Mirrors > Home > ILE Home > Th. List > abrexco | Unicode version |
Description: Composition of two image
maps ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
abrexco.1 |
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abrexco.2 |
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Ref | Expression |
---|---|
abrexco |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2423 |
. . . . 5
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2 | vex 2692 |
. . . . . . . . 9
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3 | eqeq1 2147 |
. . . . . . . . . 10
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4 | 3 | rexbidv 2439 |
. . . . . . . . 9
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5 | 2, 4 | elab 2832 |
. . . . . . . 8
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6 | 5 | anbi1i 454 |
. . . . . . 7
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7 | r19.41v 2590 |
. . . . . . 7
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8 | 6, 7 | bitr4i 186 |
. . . . . 6
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9 | 8 | exbii 1585 |
. . . . 5
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10 | 1, 9 | bitri 183 |
. . . 4
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11 | rexcom4 2712 |
. . . 4
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12 | 10, 11 | bitr4i 186 |
. . 3
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13 | abrexco.1 |
. . . . 5
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14 | abrexco.2 |
. . . . . 6
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15 | 14 | eqeq2d 2152 |
. . . . 5
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16 | 13, 15 | ceqsexv 2728 |
. . . 4
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17 | 16 | rexbii 2445 |
. . 3
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18 | 12, 17 | bitri 183 |
. 2
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19 | 18 | abbii 2256 |
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-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 |
This theorem is referenced by: restco 12382 |
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