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Mirrors > Home > ILE Home > Th. List > ovmpt2dv2 | Unicode version |
Description: Alternate deduction version of ovmpt2 5636, 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 2041 | . . 3 | |
2 | ovmpt2dv2.1 | . . . 4 | |
3 | ovmpt2dv2.2 | . . . 4 | |
4 | ovmpt2dv2.3 | . . . 4 | |
5 | ovmpt2dv2.4 | . . . . . 6 | |
6 | 5 | eqeq2d 2051 | . . . . 5 |
7 | 6 | biimpd 132 | . . . 4 |
8 | nfmpt21 5571 | . . . 4 | |
9 | nfcv 2178 | . . . . . 6 | |
10 | nfcv 2178 | . . . . . 6 | |
11 | 9, 8, 10 | nfov 5535 | . . . . 5 |
12 | 11 | nfeq1 2187 | . . . 4 |
13 | nfmpt22 5572 | . . . 4 | |
14 | nfcv 2178 | . . . . . 6 | |
15 | nfcv 2178 | . . . . . 6 | |
16 | 14, 13, 15 | nfov 5535 | . . . . 5 |
17 | 16 | nfeq1 2187 | . . . 4 |
18 | 2, 3, 4, 7, 8, 12, 13, 17 | ovmpt2df 5632 | . . 3 |
19 | 1, 18 | mpd 13 | . 2 |
20 | oveq 5518 | . . 3 | |
21 | 20 | eqeq1d 2048 | . 2 |
22 | 19, 21 | syl5ibrcom 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wcel 1393 (class class class)co 5512 cmpt2 5514 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 ax-setind 4262 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-rex 2312 df-v 2559 df-sbc 2765 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-br 3765 df-opab 3819 df-id 4030 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-iota 4867 df-fun 4904 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 |
This theorem is referenced by: (None) |
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