Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > caovdirg | Structured version Visualization version Unicode version |
Description: Convert an operation reverse distributive law to class notation. (Contributed by Mario Carneiro, 19-Oct-2014.) |
Ref | Expression |
---|---|
caovdirg.1 |
Ref | Expression |
---|---|
caovdirg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caovdirg.1 | . . 3 | |
2 | 1 | ralrimivvva 2972 | . 2 |
3 | oveq1 6657 | . . . . 5 | |
4 | 3 | oveq1d 6665 | . . . 4 |
5 | oveq1 6657 | . . . . 5 | |
6 | 5 | oveq1d 6665 | . . . 4 |
7 | 4, 6 | eqeq12d 2637 | . . 3 |
8 | oveq2 6658 | . . . . 5 | |
9 | 8 | oveq1d 6665 | . . . 4 |
10 | oveq1 6657 | . . . . 5 | |
11 | 10 | oveq2d 6666 | . . . 4 |
12 | 9, 11 | eqeq12d 2637 | . . 3 |
13 | oveq2 6658 | . . . 4 | |
14 | oveq2 6658 | . . . . 5 | |
15 | oveq2 6658 | . . . . 5 | |
16 | 14, 15 | oveq12d 6668 | . . . 4 |
17 | 13, 16 | eqeq12d 2637 | . . 3 |
18 | 7, 12, 17 | rspc3v 3325 | . 2 |
19 | 2, 18 | mpan9 486 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 (class class class)co 6650 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 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-iota 5851 df-fv 5896 df-ov 6653 |
This theorem is referenced by: caovdird 6852 srgi 18511 ringi 18560 |
Copyright terms: Public domain | W3C validator |