Theorem fdmi 5345

Description: The domain of a mapping. (Contributed by NM, 28-Jul-2008.)

Hypothesis

Ref	Expression
fdmi.1	⊢ 𝐹:𝐴⟶𝐵

Assertion

Ref	Expression
fdmi	⊢ dom 𝐹 = 𝐴

Proof of Theorem fdmi

Step	Hyp	Ref	Expression
1		fdmi.1	. 2 ⊢ 𝐹:𝐴⟶𝐵
2		fdm 5343	. 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ dom 𝐹 = 𝐴

Syntax hints:   = wceq 1343  dom cdm 4604  ⟶wf 5184

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106

This theorem depends on definitions:  df-bi 116  df-fn 5191  df-f 5192

This theorem is referenced by:  suplocexprlemdisj  7661  suplocexprlemub  7664  eluzel2  9471  inftonninf  10376  qtopbasss  13161  retopbas  13163  tgqioo  13187  dvexp  13315  efcn  13329  pilem3  13344