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Mirrors > Home > ILE Home > Th. List > uneq12i | Unicode version |
Description: Equality inference for union of two classes. (Contributed by NM, 12-Aug-2004.) (Proof shortened by Eric Schmidt, 26-Jan-2007.) |
Ref | Expression |
---|---|
uneq1i.1 |
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uneq12i.2 |
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Ref | Expression |
---|---|
uneq12i |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1i.1 |
. 2
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2 | uneq12i.2 |
. 2
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3 | uneq12 3191 |
. 2
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4 | 1, 2, 3 | mp2an 420 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-v 2659 df-un 3041 |
This theorem is referenced by: indir 3291 difundir 3295 symdif1 3307 unrab 3313 rabun2 3321 dfif6 3442 dfif3 3453 unopab 3967 xpundi 4555 xpundir 4556 xpun 4560 dmun 4706 resundi 4790 resundir 4791 cnvun 4902 rnun 4905 imaundi 4909 imaundir 4910 dmtpop 4972 coundi 4998 coundir 4999 unidmrn 5029 dfdm2 5031 mptun 5212 fpr 5556 fvsnun2 5572 sbthlemi5 6801 djuunr 6903 djuun 6904 casedm 6923 djudm 6942 djuassen 7021 fzo0to42pr 9890 |
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