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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 | |
uneq12i.2 |
Ref | Expression |
---|---|
uneq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uneq1i.1 | . 2 | |
2 | uneq12i.2 | . 2 | |
3 | uneq12 3276 | . 2 | |
4 | 1, 2, 3 | mp2an 424 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1348 cun 3119 |
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-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-un 3125 |
This theorem is referenced by: indir 3376 difundir 3380 symdif1 3392 unrab 3398 rabun2 3406 dfif6 3527 dfif3 3538 unopab 4066 xpundi 4665 xpundir 4666 xpun 4670 dmun 4816 resundi 4902 resundir 4903 cnvun 5014 rnun 5017 imaundi 5021 imaundir 5022 dmtpop 5084 coundi 5110 coundir 5111 unidmrn 5141 dfdm2 5143 mptun 5327 fpr 5675 fvsnun2 5691 sbthlemi5 6934 djuunr 7039 djuun 7040 casedm 7059 djudm 7078 djuassen 7181 fz0to3un2pr 10066 fz0to4untppr 10067 fzo0to42pr 10163 |
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