Description: The law of concretion in terms of substitutions. (Contributed by NM, 17-Mar-2008)
Ref | Expression | ||
---|---|---|---|
Hypothesis | brabsb.1 | |- R = { <. x , y >. | ph } |
|
Assertion | brabsb | |- ( A R B <-> [. A / x ]. [. B / y ]. ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brabsb.1 | |- R = { <. x , y >. | ph } |
|
2 | df-br | |- ( A R B <-> <. A , B >. e. R ) |
|
3 | 1 | eleq2i | |- ( <. A , B >. e. R <-> <. A , B >. e. { <. x , y >. | ph } ) |
4 | opelopabsb | |- ( <. A , B >. e. { <. x , y >. | ph } <-> [. A / x ]. [. B / y ]. ph ) |
|
5 | 2 3 4 | 3bitri | |- ( A R B <-> [. A / x ]. [. B / y ]. ph ) |