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Mirrors > Home > ILE Home > Th. List > eqeltrri | Unicode version |
Description: Substitution of equal classes into membership relation. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
eqeltrr.1 | |
eqeltrr.2 |
Ref | Expression |
---|---|
eqeltrri |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeltrr.1 | . . 3 | |
2 | 1 | eqcomi 2168 | . 2 |
3 | eqeltrr.2 | . 2 | |
4 | 2, 3 | eqeltri 2237 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 |
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-5 1434 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-4 1497 ax-17 1513 ax-ial 1521 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-cleq 2157 df-clel 2160 |
This theorem is referenced by: 3eltr3i 2245 p0ex 4161 epse 4314 unex 4413 ordtri2orexmid 4494 onsucsssucexmid 4498 ordsoexmid 4533 ordtri2or2exmid 4542 ontri2orexmidim 4543 nnregexmid 4592 abrexex 6077 opabex3 6082 abrexex2 6084 abexssex 6085 abexex 6086 oprabrexex2 6090 tfr0dm 6281 exmidonfinlem 7140 1lt2pi 7272 prarloclemarch2 7351 prarloclemlt 7425 0cn 7882 resubcli 8152 0reALT 8186 10nn 9328 numsucc 9352 nummac 9357 qreccl 9571 unirnioo 9900 fz0to4untppr 10049 sn0topon 12635 retopbas 13070 blssioo 13092 bj-unex 13642 exmidsbthrlem 13742 |
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