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Mirrors > Home > MPE Home > Th. List > f1o2d | Structured version Visualization version Unicode version |
Description: Describe an implicit one-to-one onto function. (Contributed by Mario Carneiro, 12-May-2014.) |
Ref | Expression |
---|---|
f1od.1 |
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f1o2d.2 |
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f1o2d.3 |
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f1o2d.4 |
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Ref | Expression |
---|---|
f1o2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1od.1 |
. . 3
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2 | f1o2d.2 |
. . 3
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3 | f1o2d.3 |
. . 3
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4 | f1o2d.4 |
. . 3
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5 | 1, 2, 3, 4 | f1ocnv2d 6546 |
. 2
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6 | 5 | simpld 465 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-rab 2757 df-v 3058 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-br 4416 df-opab 4475 df-mpt 4476 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 |
This theorem is referenced by: f1opw2 6548 en3d 7631 f1opwfi 7903 mapfien 7946 fin23lem22 8782 incexclem 13942 grplmulf1o 16776 conjghm 16961 gapm 17008 psrbagconf1o 18646 hmeoimaf1o 20833 itg1mulc 22710 resinf1o 23533 eff1olem 23545 sqff1o 24157 dvdsflip 24159 dvdsppwf1o 24163 dvdsflf1o 24164 fcobij 28358 hashgcdlem 36118 |
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