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Mirrors > Home > ILE Home > Th. List > ensym | Unicode version |
Description: Symmetry of equinumerosity. Theorem 2 of [Suppes] p. 92. (Contributed by NM, 26-Oct-2003.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
ensym |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ensymb 6754 | . 2 | |
2 | 1 | biimpi 119 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 class class class wbr 3987 cen 6712 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-13 2143 ax-14 2144 ax-ext 2152 ax-sep 4105 ax-pow 4158 ax-pr 4192 ax-un 4416 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3566 df-sn 3587 df-pr 3588 df-op 3590 df-uni 3795 df-br 3988 df-opab 4049 df-id 4276 df-xp 4615 df-rel 4616 df-cnv 4617 df-co 4618 df-dm 4619 df-rn 4620 df-res 4621 df-ima 4622 df-fun 5198 df-fn 5199 df-f 5200 df-f1 5201 df-fo 5202 df-f1o 5203 df-er 6509 df-en 6715 |
This theorem is referenced by: ensymi 6756 ensymd 6757 enen1 6814 enen2 6815 domen1 6816 domen2 6817 nneneq 6831 ssfilem 6849 diffitest 6861 fiintim 6902 fisseneq 6905 en1eqsn 6921 fidcenumlemim 6925 enomni 7111 enmkv 7134 enwomni 7142 finnum 7147 pr2ne 7156 djucomen 7180 cc2lem 7215 enct 12375 |
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