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Mirrors > Home > ILE Home > Th. List > ensymd | Unicode version |
Description: Symmetry of equinumerosity. Deduction form of ensym 6643. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
ensymd.1 |
Ref | Expression |
---|---|
ensymd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ensymd.1 | . 2 | |
2 | ensym 6643 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 class class class wbr 3899 cen 6600 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-er 6397 df-en 6603 |
This theorem is referenced by: f1imaeng 6654 f1imaen2g 6655 en2sn 6675 xpdom3m 6696 phplem4 6717 phplem4dom 6724 php5dom 6725 phpm 6727 phplem4on 6729 dif1en 6741 dif1enen 6742 fisbth 6745 fin0 6747 fin0or 6748 fientri3 6771 unsnfidcex 6776 unsnfidcel 6777 fiintim 6785 fisseneq 6788 f1ofi 6799 endjusym 6949 eninl 6950 eninr 6951 pm54.43 7014 djuen 7035 dju1en 7037 djuassen 7041 xpdjuen 7042 uzenom 10166 hashennnuni 10493 hashennn 10494 hashcl 10495 hashfz1 10497 hashen 10498 fihashfn 10514 fihashdom 10517 hashunlem 10518 zfz1iso 10552 summodclem2 11119 zsumdc 11121 ennnfonelemen 11861 exmidunben 11866 ctinfom 11868 ctinf 11870 pwf1oexmid 13121 sbthom 13148 |
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