Description: If two elements are connected by a value of the identity relation, then they are connected via the argument. (Contributed by RP, 21-Jul-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | brfvid.r | |- ( ph -> R e. _V ) |
|
Assertion | brfvid | |- ( ph -> ( A ( _I ` R ) B <-> A R B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | brfvid.r | |- ( ph -> R e. _V ) |
|
2 | fvi | |- ( R e. _V -> ( _I ` R ) = R ) |
|
3 | 1 2 | syl | |- ( ph -> ( _I ` R ) = R ) |
4 | 3 | breqd | |- ( ph -> ( A ( _I ` R ) B <-> A R B ) ) |