Description: The proper substitution of an ordered pair for a setvar variable corresponds to a proper substitution of each of its components. (Contributed by AV, 8-Apr-2023)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sbcop.z | |
|
Assertion | sbcop | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcop.z | |
|
2 | 1 | sbcop1 | |
3 | 2 | sbcbii | |
4 | sbcnestgw | |
|
5 | 4 | elv | |
6 | csbopg | |
|
7 | 6 | elv | |
8 | vex | |
|
9 | 8 | csbconstgi | |
10 | 8 | csbvargi | |
11 | 9 10 | opeq12i | |
12 | 7 11 | eqtri | |
13 | dfsbcq | |
|
14 | 12 13 | ax-mp | |
15 | 3 5 14 | 3bitri | |