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Mirrors > Home > ILE Home > Th. List > elecg | Unicode version |
Description: Membership in an equivalence class. Theorem 72 of [Suppes] p. 82. (Contributed by Mario Carneiro, 9-Jul-2014.) |
Ref | Expression |
---|---|
elecg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elimasng 4966 | . . 3 | |
2 | 1 | ancoms 266 | . 2 |
3 | df-ec 6494 | . . 3 | |
4 | 3 | eleq2i 2231 | . 2 |
5 | df-br 3977 | . 2 | |
6 | 2, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 2135 csn 3570 cop 3573 class class class wbr 3976 cima 4601 cec 6490 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-br 3977 df-opab 4038 df-xp 4604 df-cnv 4606 df-dm 4608 df-rn 4609 df-res 4610 df-ima 4611 df-ec 6494 |
This theorem is referenced by: elec 6531 relelec 6532 ecdmn0m 6534 erth 6536 ecidg 6556 qsel 6569 xmetec 12978 blpnfctr 12980 xmetresbl 12981 |
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