Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > f1of1 | GIF version |
Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by NM, 12-Dec-2003.) |
Ref | Expression |
---|---|
f1of1 | ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹:𝐴–1-1→𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-f1o 4929 | . 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 ↔ (𝐹:𝐴–1-1→𝐵 ∧ 𝐹:𝐴–onto→𝐵)) | |
2 | 1 | simplbi 268 | 1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹:𝐴–1-1→𝐵) |
Colors of variables: wff set class |
Syntax hints: → wi 4 –1-1→wf1 4919 –onto→wfo 4920 –1-1-onto→wf1o 4921 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 |
This theorem depends on definitions: df-bi 115 df-f1o 4929 |
This theorem is referenced by: f1of 5146 f1oresrab 5350 f1ocnvfvrneq 5442 isores3 5475 isoini2 5478 f1oiso 5485 f1opw2 5726 tposf12 5907 enssdom 6265 phplem4 6341 phplem4on 6353 fidceq 6354 en2eqpr 6380 isotilem 6419 negfi 10110 |
Copyright terms: Public domain | W3C validator |