Theorem f1oen

Description: The domain and range of a one-to-one, onto function are equinumerous. (Contributed by NM, 19-Jun-1998)

	Ref	Expression
Hypothesis	f1oen.1	$$⊢A\in \mathrm{V}$$
Assertion	f1oen	$$⊢F:A\underset{1-1\; onto}{⟶}B\to A\approx B$$

Proof

Step	Hyp	Ref	Expression
1		f1oen.1	$$⊢A\in \mathrm{V}$$
2		f1oeng	$$⊢\left(A\in \mathrm{V}\wedge F:A\underset{1-1\; onto}{⟶}B\right)\to A\approx B$$
3	1 2	mpan	$$⊢F:A\underset{1-1\; onto}{⟶}B\to A\approx B$$