Theorem fdmi 5544

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 5542	. 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ dom 𝐹 = 𝐴

This proof depends on syntax axioms:   = wceq 1402  dom cdm 4776  ⟶wf 5376

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This proof depends on definitions:  df-bi 117  df-fn 5383  df-f 5384

This theorem is used by:  suplocexprlemdisj  8093  suplocexprlemub  8096  eluzel2  9941  inftonninf  10899  qtopbasss  15764  retopbas  15766  tgqioo  15798  dvexp  15954  efcn  16011  pilem3  16027