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Mirrors > Home > MPE Home > Th. List > fssxp | Structured version Visualization version Unicode version |
Description: A mapping is a class of ordered pairs. (Contributed by NM, 3-Aug-1994.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) |
Ref | Expression |
---|---|
fssxp |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frel 5730 |
. . 3
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2 | relssdmrn 5355 |
. . 3
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3 | 1, 2 | syl 17 |
. 2
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4 | fdm 5731 |
. . . 4
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5 | eqimss 3483 |
. . . 4
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6 | 4, 5 | syl 17 |
. . 3
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7 | frn 5733 |
. . 3
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8 | xpss12 4939 |
. . 3
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9 | 6, 7, 8 | syl2anc 666 |
. 2
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10 | 3, 9 | sstrd 3441 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pr 4638 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-br 4402 df-opab 4461 df-xp 4839 df-rel 4840 df-cnv 4841 df-dm 4843 df-rn 4844 df-fun 5583 df-fn 5584 df-f 5585 |
This theorem is referenced by: funssxp 5740 opelf 5743 dff2 6032 dff3 6033 fndifnfp 6091 fex2 6745 fabexg 6746 f2ndf 6899 f1o2ndf1 6901 mapex 7475 uniixp 7542 hartogslem1 8054 wdom2d 8092 rankfu 8345 dfac12lem2 8571 infmap2 8645 axdc3lem 8877 tskcard 9203 dfle2 11443 ixxex 11643 imasvscafn 15436 imasvscaf 15438 fnmrc 15506 mrcfval 15507 isacs1i 15556 mreacs 15557 pjfval 19262 pjpm 19264 hausdiag 20653 isngp2 21604 volf 22476 fnct 28290 fgraphopab 36081 |
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