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Mirrors > Home > ILE Home > Th. List > opeq1 | Unicode version |
Description: Equality theorem for ordered pairs. (Contributed by NM, 25-Jun-1998.) (Revised by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2100 | . . . . . 6 | |
2 | 1 | anbi1d 438 | . . . . 5 |
3 | sneq 3386 | . . . . . . 7 | |
4 | preq1 3447 | . . . . . . 7 | |
5 | 3, 4 | preq12d 3455 | . . . . . 6 |
6 | 5 | eleq2d 2107 | . . . . 5 |
7 | 2, 6 | anbi12d 442 | . . . 4 |
8 | df-3an 887 | . . . 4 | |
9 | df-3an 887 | . . . 4 | |
10 | 7, 8, 9 | 3bitr4g 212 | . . 3 |
11 | 10 | abbidv 2155 | . 2 |
12 | df-op 3384 | . 2 | |
13 | df-op 3384 | . 2 | |
14 | 11, 12, 13 | 3eqtr4g 2097 | 1 |
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