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Mirrors > Home > ILE Home > Th. List > ensymd | Unicode version |
Description: Symmetry of equinumerosity. Deduction form of ensym 6738. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
ensymd.1 |
Ref | Expression |
---|---|
ensymd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ensymd.1 | . 2 | |
2 | ensym 6738 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 class class class wbr 3976 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-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 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-uni 3784 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-fun 5184 df-fn 5185 df-f 5186 df-f1 5187 df-fo 5188 df-f1o 5189 df-er 6492 df-en 6698 |
This theorem is referenced by: f1imaeng 6749 f1imaen2g 6750 en2sn 6770 xpdom3m 6791 phplem4 6812 phplem4dom 6819 php5dom 6820 phpm 6822 phplem4on 6824 dif1en 6836 dif1enen 6837 fisbth 6840 fin0 6842 fin0or 6843 fientri3 6871 unsnfidcex 6876 unsnfidcel 6877 fiintim 6885 fisseneq 6888 f1ofi 6899 endjusym 7052 eninl 7053 eninr 7054 pm54.43 7137 djuen 7158 dju1en 7160 djuassen 7164 xpdjuen 7165 uzenom 10350 hashennnuni 10681 hashennn 10682 hashcl 10683 hashfz1 10685 hashen 10686 fihashfn 10702 fihashdom 10705 hashunlem 10706 zfz1iso 10740 summodclem2 11309 zsumdc 11311 prodmodclem2 11504 zproddc 11506 ennnfonelemen 12297 exmidunben 12302 ctinfom 12304 ctinf 12306 pwf1oexmid 13720 sbthom 13746 |
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