Theorem fdmOLD 6737

Description: Obsolete version of fdm 6736 as of 29-May-2024. (Contributed by NM, 2-Aug-1994.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
fdmOLD	⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)

Proof of Theorem fdmOLD

Step	Hyp	Ref	Expression
1		ffn 6727	. 2 ⊢ (𝐹:𝐴⟶𝐵 → 𝐹 Fn 𝐴)
2		fndm 6662	. 2 ⊢ (𝐹 Fn 𝐴 → dom 𝐹 = 𝐴)
3	1, 2	syl 17	1 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)

Syntax hints:   → wi 4   = wceq 1533  dom cdm 5682   Fn wfn 6548  ⟶wf 6549

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 206  df-an 395  df-fn 6556  df-f 6557

This theorem is referenced by: (None)