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Mirrors > Home > ILE Home > Th. List > ovmpodv2 | Unicode version |
Description: Alternate deduction version of ovmpo 5968, 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 2165 | . . 3 | |
2 | ovmpodv2.1 | . . . 4 | |
3 | ovmpodv2.2 | . . . 4 | |
4 | ovmpodv2.3 | . . . 4 | |
5 | ovmpodv2.4 | . . . . . 6 | |
6 | 5 | eqeq2d 2176 | . . . . 5 |
7 | 6 | biimpd 143 | . . . 4 |
8 | nfmpo1 5900 | . . . 4 | |
9 | nfcv 2306 | . . . . . 6 | |
10 | nfcv 2306 | . . . . . 6 | |
11 | 9, 8, 10 | nfov 5863 | . . . . 5 |
12 | 11 | nfeq1 2316 | . . . 4 |
13 | nfmpo2 5901 | . . . 4 | |
14 | nfcv 2306 | . . . . . 6 | |
15 | nfcv 2306 | . . . . . 6 | |
16 | 14, 13, 15 | nfov 5863 | . . . . 5 |
17 | 16 | nfeq1 2316 | . . . 4 |
18 | 2, 3, 4, 7, 8, 12, 13, 17 | ovmpodf 5964 | . . 3 |
19 | 1, 18 | mpd 13 | . 2 |
20 | oveq 5842 | . . 3 | |
21 | 20 | eqeq1d 2173 | . 2 |
22 | 19, 21 | syl5ibrcom 156 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1342 wcel 2135 (class class class)co 5836 cmpo 5838 |
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 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-setind 4508 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-ov 5839 df-oprab 5840 df-mpo 5841 |
This theorem is referenced by: (None) |
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