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Mirrors > Home > MPE Home > Th. List > Mathboxes > stoweidlem8 | Structured version Visualization version Unicode version |
Description: Lemma for stoweid 40280: two class variables replace two setvar variables, for the sum of two functions. (Contributed by Glauco Siliprandi, 20-Apr-2017.) |
Ref | Expression |
---|---|
stoweidlem8.1 | |
stoweidlem8.2 | |
stoweidlem8.3 |
Ref | Expression |
---|---|
stoweidlem8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 1063 | . 2 | |
2 | eleq1 2689 | . . . . 5 | |
3 | 2 | 3anbi3d 1405 | . . . 4 |
4 | stoweidlem8.3 | . . . . . . 7 | |
5 | 4 | nfeq2 2780 | . . . . . 6 |
6 | fveq1 6190 | . . . . . . . 8 | |
7 | 6 | oveq2d 6666 | . . . . . . 7 |
8 | 7 | adantr 481 | . . . . . 6 |
9 | 5, 8 | mpteq2da 4743 | . . . . 5 |
10 | 9 | eleq1d 2686 | . . . 4 |
11 | 3, 10 | imbi12d 334 | . . 3 |
12 | simp2 1062 | . . . 4 | |
13 | eleq1 2689 | . . . . . . 7 | |
14 | 13 | 3anbi2d 1404 | . . . . . 6 |
15 | stoweidlem8.2 | . . . . . . . . 9 | |
16 | 15 | nfeq2 2780 | . . . . . . . 8 |
17 | fveq1 6190 | . . . . . . . . . 10 | |
18 | 17 | oveq1d 6665 | . . . . . . . . 9 |
19 | 18 | adantr 481 | . . . . . . . 8 |
20 | 16, 19 | mpteq2da 4743 | . . . . . . 7 |
21 | 20 | eleq1d 2686 | . . . . . 6 |
22 | 14, 21 | imbi12d 334 | . . . . 5 |
23 | stoweidlem8.1 | . . . . 5 | |
24 | 22, 23 | vtoclg 3266 | . . . 4 |
25 | 12, 24 | mpcom 38 | . . 3 |
26 | 11, 25 | vtoclg 3266 | . 2 |
27 | 1, 26 | mpcom 38 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 w3a 1037 wceq 1483 wcel 1990 wnfc 2751 cmpt 4729 cfv 5888 (class class class)co 6650 caddc 9939 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 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-uni 4437 df-br 4654 df-opab 4713 df-mpt 4730 df-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: stoweidlem20 40237 stoweidlem21 40238 stoweidlem22 40239 stoweidlem23 40240 |
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