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Mirrors > Home > ILE Home > Th. List > ovmpt2dv2 | Unicode version |
Description: Alternate deduction version of ovmpt2 5656, suitable for iteration. (Contributed by Mario Carneiro, 7-Jan-2017.) |
Ref | Expression |
---|---|
ovmpt2dv2.1 | |
ovmpt2dv2.2 | |
ovmpt2dv2.3 | |
ovmpt2dv2.4 |
Ref | Expression |
---|---|
ovmpt2dv2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2082 | . . 3 | |
2 | ovmpt2dv2.1 | . . . 4 | |
3 | ovmpt2dv2.2 | . . . 4 | |
4 | ovmpt2dv2.3 | . . . 4 | |
5 | ovmpt2dv2.4 | . . . . . 6 | |
6 | 5 | eqeq2d 2092 | . . . . 5 |
7 | 6 | biimpd 142 | . . . 4 |
8 | nfmpt21 5591 | . . . 4 | |
9 | nfcv 2219 | . . . . . 6 | |
10 | nfcv 2219 | . . . . . 6 | |
11 | 9, 8, 10 | nfov 5555 | . . . . 5 |
12 | 11 | nfeq1 2228 | . . . 4 |
13 | nfmpt22 5592 | . . . 4 | |
14 | nfcv 2219 | . . . . . 6 | |
15 | nfcv 2219 | . . . . . 6 | |
16 | 14, 13, 15 | nfov 5555 | . . . . 5 |
17 | 16 | nfeq1 2228 | . . . 4 |
18 | 2, 3, 4, 7, 8, 12, 13, 17 | ovmpt2df 5652 | . . 3 |
19 | 1, 18 | mpd 13 | . 2 |
20 | oveq 5538 | . . 3 | |
21 | 20 | eqeq1d 2089 | . 2 |
22 | 19, 21 | syl5ibrcom 155 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wceq 1284 wcel 1433 (class class class)co 5532 cmpt2 5534 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 576 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-pow 3948 ax-pr 3964 ax-setind 4280 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-fal 1290 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-v 2603 df-sbc 2816 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-br 3786 df-opab 3840 df-id 4048 df-xp 4369 df-rel 4370 df-cnv 4371 df-co 4372 df-dm 4373 df-iota 4887 df-fun 4924 df-fv 4930 df-ov 5535 df-oprab 5536 df-mpt2 5537 |
This theorem is referenced by: (None) |
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