Theorem f1odmOLD 6825

Description: Obsolete version of f1odm 6824 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–1-1-onto→𝐵 → dom 𝐹 = 𝐴)

Proof of Theorem f1odmOLD

Step	Hyp	Ref	Expression
1		f1ofn 6821	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹 Fn 𝐴)
2		fndm 6638	. 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
3	1, 2	syl 18	1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → dom 𝐹 = 𝐴)

Syntax hints:   → wi 4   = wceq 1568  dom cdm 5661   Fn wfn 6531  –1-1-onto→wf1o 6535

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 401  df-fn 6539  df-f 6540  df-f1 6541  df-f1o 6543

This theorem is referenced by: (None)