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Mirrors > Home > ILE Home > Th. List > mapprc | Unicode version |
Description: When ![]() ![]() ![]() |
Ref | Expression |
---|---|
mapprc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abn0m 3460 |
. . . 4
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2 | fdm 5383 |
. . . . . 6
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3 | vex 2752 |
. . . . . . 7
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4 | 3 | dmex 4905 |
. . . . . 6
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5 | 2, 4 | eqeltrrdi 2279 |
. . . . 5
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6 | 5 | exlimiv 1608 |
. . . 4
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7 | 1, 6 | sylbi 121 |
. . 3
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8 | 7 | con3i 633 |
. 2
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9 | notm0 3455 |
. 2
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10 | 8, 9 | sylib 122 |
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-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2160 ax-14 2161 ax-ext 2169 ax-sep 4133 ax-pow 4186 ax-pr 4221 ax-un 4445 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2039 df-mo 2040 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-rex 2471 df-v 2751 df-dif 3143 df-un 3145 df-in 3147 df-ss 3154 df-nul 3435 df-pw 3589 df-sn 3610 df-pr 3611 df-op 3613 df-uni 3822 df-br 4016 df-opab 4077 df-cnv 4646 df-dm 4648 df-rn 4649 df-fn 5231 df-f 5232 |
This theorem is referenced by: (None) |
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