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Mirrors > Home > ILE Home > Th. List > relen | GIF version |
Description: Equinumerosity is a relation. (Contributed by NM, 28-Mar-1998.) |
Ref | Expression |
---|---|
relen | ⊢ Rel ≈ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-en 6698 | . 2 ⊢ ≈ = {〈𝑥, 𝑦〉 ∣ ∃𝑓 𝑓:𝑥–1-1-onto→𝑦} | |
2 | 1 | relopabi 4724 | 1 ⊢ Rel ≈ |
Colors of variables: wff set class |
Syntax hints: ∃wex 1479 Rel wrel 4603 –1-1-onto→wf1o 5181 ≈ cen 6695 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-opab 4038 df-xp 4604 df-rel 4605 df-en 6698 |
This theorem is referenced by: encv 6703 isfi 6718 enssdom 6719 ener 6736 en1uniel 6761 xpen 6802 enomnilem 7093 enmkvlem 7116 enwomnilem 7124 djuenun 7159 cc3 7200 pwf1oexmid 13720 |
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