Theorem f1odmOLD 6832

Description: Obsolete version of f1odm 6831 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 6828	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → 𝐹 Fn 𝐴)
2		fndm 6645	. 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
3	1, 2	syl 18	1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → dom 𝐹 = 𝐴)

This proof depends on syntax axioms:   → wi 4   = wceq 1570  dom cdm 5666   Fn wfn 6538  –1-1-onto→wf1o 6542

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 6546  df-f 6547  df-f1 6548  df-f1o 6550

This theorem is used by: (None)