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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 2141 | . 2 |
3 | eqeltrr.2 | . 2 | |
4 | 2, 3 | eqeltri 2210 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-clel 2133 |
This theorem is referenced by: 3eltr3i 2218 p0ex 4107 epse 4259 unex 4357 ordtri2orexmid 4433 onsucsssucexmid 4437 ordsoexmid 4472 ordtri2or2exmid 4481 nnregexmid 4529 abrexex 6008 opabex3 6013 abrexex2 6015 abexssex 6016 abexex 6017 oprabrexex2 6021 tfr0dm 6212 exmidonfinlem 7042 1lt2pi 7141 prarloclemarch2 7220 prarloclemlt 7294 0cn 7751 resubcli 8018 0reALT 8052 10nn 9190 numsucc 9214 nummac 9219 qreccl 9427 unirnioo 9749 sn0topon 12246 retopbas 12681 blssioo 12703 bj-unex 13106 nninffeq 13205 exmidsbthrlem 13206 |
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