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Mirrors > Home > MPE Home > Th. List > ovig | Structured version Visualization version Unicode version |
Description: The value of an operation class abstraction (weak version). (Unnecessary distinct variable restrictions were removed by David Abernethy, 19-Jun-2012.) (Contributed by NM, 14-Sep-1999.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ovig.1 | |
ovig.2 | |
ovig.3 |
Ref | Expression |
---|---|
ovig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simpa 1058 | . 2 | |
2 | eleq1 2689 | . . . . . 6 | |
3 | eleq1 2689 | . . . . . 6 | |
4 | 2, 3 | bi2anan9 917 | . . . . 5 |
5 | 4 | 3adant3 1081 | . . . 4 |
6 | ovig.1 | . . . 4 | |
7 | 5, 6 | anbi12d 747 | . . 3 |
8 | ovig.2 | . . . 4 | |
9 | moanimv 2531 | . . . 4 | |
10 | 8, 9 | mpbir 221 | . . 3 |
11 | ovig.3 | . . 3 | |
12 | 7, 10, 11 | ovigg 6781 | . 2 |
13 | 1, 12 | mpand 711 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 w3a 1037 wceq 1483 wcel 1990 wmo 2471 (class class class)co 6650 coprab 6651 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-eu 2474 df-mo 2475 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-sbc 3436 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-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 |
This theorem is referenced by: addsrpr 9896 mulsrpr 9897 |
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