Theorem f1odmOLD 6851

Description: Obsolete version of f1odm 6850 as of 10-Jun-2026. (Contributed by NM, 8-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
f1odmOLD	⊢ (𝐹:𝐴⟶1-1onto𝐵 → dom 𝐹 = 𝐴)

Proof of Theorem f1odmOLD

Step	Hyp	Ref	Expression
1		f1ofn 6847	. 2 ⊢ (𝐹:𝐴⟶1-1onto𝐵 → 𝐹 Fn 𝐴)
2		fndm 6664	. 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
3	1, 2	syl 18	1 ⊢ (𝐹:𝐴⟶1-1onto𝐵 → dom 𝐹 = 𝐴)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  dom cdm 5655   Fn wfn 6553  ⟶1-1ontowf1o 6557

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-fn 6561  df-f 6562  df-f1 6563  df-f1o 6565

This theorem is used by: (None)