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Mirrors > Home > MPE Home > Th. List > elecg | Structured version Visualization version 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 5491 | . . 3 | |
2 | 1 | ancoms 469 | . 2 |
3 | df-ec 7744 | . . 3 | |
4 | 3 | eleq2i 2693 | . 2 |
5 | df-br 4654 | . 2 | |
6 | 2, 4, 5 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wcel 1990 csn 4177 cop 4183 class class class wbr 4653 cima 5117 cec 7740 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-ec 7744 |
This theorem is referenced by: elec 7786 relelec 7787 ecdmn0 7789 erth 7791 erdisj 7794 qsel 7826 orbsta 17746 sylow2alem1 18032 sylow2blem1 18035 sylow3lem3 18044 efgi2 18138 tgpconncompeqg 21915 xmetec 22239 blpnfctr 22241 xmetresbl 22242 xrsblre 22614 ecin0 34117 |
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