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Mirrors > Home > ILE Home > Th. List > entr | Unicode version |
Description: Transitivity of equinumerosity. Theorem 3 of [Suppes] p. 92. (Contributed by NM, 9-Jun-1998.) |
Ref | Expression |
---|---|
entr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ener 6282 | . . . 4 | |
2 | 1 | a1i 9 | . . 3 |
3 | 2 | ertr 6144 | . 2 |
4 | 3 | trud 1293 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wtru 1285 cvv 2601 class class class wbr 3785 wer 6126 cen 6242 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-un 4188 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-rn 4374 df-res 4375 df-ima 4376 df-fun 4924 df-fn 4925 df-f 4926 df-f1 4927 df-fo 4928 df-f1o 4929 df-er 6129 df-en 6245 |
This theorem is referenced by: entri 6289 en2sn 6313 xpsnen2g 6326 enen1 6334 enen2 6335 phplem4 6341 snnen2og 6345 php5dom 6349 phplem4on 6353 dif1en 6364 fisbth 6367 diffisn 6377 unsnfidcex 6385 unsnfidcel 6386 carden2bex 6458 pm54.43 6459 pr2ne 6461 frecfzen2 9420 1nprm 10496 |
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