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| Mirrors > Home > MPE Home > Th. List > relen | Structured version Visualization version GIF version | ||
| Description: Equinumerosity is a relation. (Contributed by NM, 28-Mar-1998.) |
| Ref | Expression |
|---|---|
| relen | ⊢ Rel ≈ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-en 8986 | . 2 ⊢ ≈ = {〈𝑥, 𝑦〉 ∣ ∃𝑓 𝑓:𝑥–1-1-onto→𝑦} | |
| 2 | 1 | relopabiv 5830 | 1 ⊢ Rel ≈ |
| Colors of variables: wff setvar class |
| Syntax hints: ∃wex 1779 Rel wrel 5690 –1-1-onto→wf1o 6560 ≈ cen 8982 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-ss 3968 df-opab 5206 df-xp 5691 df-rel 5692 df-en 8986 |
| This theorem is referenced by: encv 8993 isfi 9016 enssdom 9017 ener 9041 enfixsn 9121 sbthcl 9135 xpen 9180 pwen 9190 php3OLD 9261 f1finf1oOLD 9306 mapfien2 9449 isnum2 9985 inffien 10103 djuen 10210 djuenun 10211 cdainflem 10228 djulepw 10233 infmap2 10257 fin4i 10338 fin4en1 10349 isfin4p1 10355 enfin2i 10361 fin45 10432 axcc3 10478 engch 10668 hargch 10713 hasheni 14387 pmtrfv 19470 frgpcyg 21592 lbslcic 21861 phpreu 37611 ctbnfien 42829 |
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