Description: Substitution of equal classes into membership relation. (Contributed by NM, 21-Jun-1993)
Ref | Expression | ||
---|---|---|---|
Hypotheses | eqeltri.1 | |- A = B |
|
eqeltri.2 | |- B e. C |
||
Assertion | eqeltri | |- A e. C |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeltri.1 | |- A = B |
|
2 | eqeltri.2 | |- B e. C |
|
3 | 1 | eleq1i | |- ( A e. C <-> B e. C ) |
4 | 2 3 | mpbir | |- A e. C |