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Mirrors > Home > MPE Home > Th. List > Mathboxes > ddeval1 | Structured version Visualization version Unicode version |
Description: Value of the delta measure. (Contributed by Thierry Arnoux, 14-Sep-2018.) |
Ref | Expression |
---|---|
ddeval1 | δ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | reex 10027 | . . . . 5 | |
2 | 1 | ssex 4802 | . . . 4 |
3 | elpwg 4166 | . . . . 5 | |
4 | 3 | biimpar 502 | . . . 4 |
5 | 2, 4 | mpancom 703 | . . 3 |
6 | eleq2 2690 | . . . . 5 | |
7 | 6 | ifbid 4108 | . . . 4 |
8 | df-dde 30296 | . . . 4 δ | |
9 | 1ex 10035 | . . . . 5 | |
10 | c0ex 10034 | . . . . 5 | |
11 | 9, 10 | ifex 4156 | . . . 4 |
12 | 7, 8, 11 | fvmpt 6282 | . . 3 δ |
13 | 5, 12 | syl 17 | . 2 δ |
14 | iftrue 4092 | . 2 | |
15 | 13, 14 | sylan9eq 2676 | 1 δ |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 cvv 3200 wss 3574 cif 4086 cpw 4158 cfv 5888 cr 9935 cc0 9936 c1 9937 δcdde 30295 |
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 ax-cnex 9992 ax-resscn 9993 ax-1cn 9994 ax-icn 9995 ax-addcl 9996 ax-mulcl 9998 ax-i2m1 10004 |
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-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-dde 30296 |
This theorem is referenced by: ddemeas 30299 |
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