Description: Equality deduction for one-to-one onto functions. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Hypothesis | f1oeq3d.1 | |- ( ph -> A = B ) |
|
Assertion | f1oeq3d | |- ( ph -> ( F : C -1-1-onto-> A <-> F : C -1-1-onto-> B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1oeq3d.1 | |- ( ph -> A = B ) |
|
2 | f1oeq3 | |- ( A = B -> ( F : C -1-1-onto-> A <-> F : C -1-1-onto-> B ) ) |
|
3 | 1 2 | syl | |- ( ph -> ( F : C -1-1-onto-> A <-> F : C -1-1-onto-> B ) ) |