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Mirrors > Home > ILE Home > Th. List > ovmpodv2 | Unicode version |
Description: Alternate deduction version of ovmpo 5906, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.) |
Ref | Expression |
---|---|
ovmpodv2.1 | |
ovmpodv2.2 | |
ovmpodv2.3 | |
ovmpodv2.4 |
Ref | Expression |
---|---|
ovmpodv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2140 | . . 3 | |
2 | ovmpodv2.1 | . . . 4 | |
3 | ovmpodv2.2 | . . . 4 | |
4 | ovmpodv2.3 | . . . 4 | |
5 | ovmpodv2.4 | . . . . . 6 | |
6 | 5 | eqeq2d 2151 | . . . . 5 |
7 | 6 | biimpd 143 | . . . 4 |
8 | nfmpo1 5838 | . . . 4 | |
9 | nfcv 2281 | . . . . . 6 | |
10 | nfcv 2281 | . . . . . 6 | |
11 | 9, 8, 10 | nfov 5801 | . . . . 5 |
12 | 11 | nfeq1 2291 | . . . 4 |
13 | nfmpo2 5839 | . . . 4 | |
14 | nfcv 2281 | . . . . . 6 | |
15 | nfcv 2281 | . . . . . 6 | |
16 | 14, 13, 15 | nfov 5801 | . . . . 5 |
17 | 16 | nfeq1 2291 | . . . 4 |
18 | 2, 3, 4, 7, 8, 12, 13, 17 | ovmpodf 5902 | . . 3 |
19 | 1, 18 | mpd 13 | . 2 |
20 | oveq 5780 | . . 3 | |
21 | 20 | eqeq1d 2148 | . 2 |
22 | 19, 21 | syl5ibrcom 156 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1331 wcel 1480 (class class class)co 5774 cmpo 5776 |
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-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 ax-setind 4452 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ne 2309 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-dif 3073 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-ov 5777 df-oprab 5778 df-mpo 5779 |
This theorem is referenced by: (None) |
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