Theorem f1dmOLD 6565

Description: Obsolete version of f1dm 6564 as of 29-May-2024. (Contributed by NM, 8-Mar-2014.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
f1dmOLD	⊢ (𝐹:𝐴–1-1→𝐵 → dom 𝐹 = 𝐴)

Proof of Theorem f1dmOLD

Step	Hyp	Ref	Expression
1		f1fn 6561	. 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴)
2		fndm 6436	. 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
3	1, 2	syl 17	1 ⊢ (𝐹:𝐴–1-1→𝐵 → dom 𝐹 = 𝐴)

Syntax hints:   → wi 4   = wceq 1538  dom cdm 5524   Fn wfn 6330  –1-1→wf1 6332

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 400  df-fn 6338  df-f 6339  df-f1 6340

This theorem is referenced by: (None)