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Mirrors > Home > MPE Home > Th. List > Mathboxes > coep | Structured version Visualization version Unicode version |
Description: Composition with epsilon. (Contributed by Scott Fenton, 18-Feb-2013.) |
Ref | Expression |
---|---|
coep.1 | |
coep.2 |
Ref | Expression |
---|---|
coep |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coep.2 | . . . . . 6 | |
2 | 1 | epelc 5031 | . . . . 5 |
3 | 2 | anbi2i 730 | . . . 4 |
4 | ancom 466 | . . . 4 | |
5 | 3, 4 | bitri 264 | . . 3 |
6 | 5 | exbii 1774 | . 2 |
7 | coep.1 | . . 3 | |
8 | 7, 1 | brco 5292 | . 2 |
9 | df-rex 2918 | . 2 | |
10 | 6, 8, 9 | 3bitr4i 292 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wex 1704 wcel 1990 wrex 2913 cvv 3200 class class class wbr 4653 cep 5028 ccom 5118 |
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-ne 2795 df-rex 2918 df-rab 2921 df-v 3202 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-eprel 5029 df-co 5123 |
This theorem is referenced by: dffr5 31643 brbigcup 32005 elfuns 32022 brimage 32033 |
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