Theorem fdmi 5484

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 5482	. 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ dom 𝐹 = 𝐴

Syntax hints:   = wceq 1395  dom cdm 4720  ⟶wf 5317

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107

This theorem depends on definitions:  df-bi 117  df-fn 5324  df-f 5325

This theorem is referenced by:  suplocexprlemdisj  7923  suplocexprlemub  7926  eluzel2  9743  inftonninf  10681  qtopbasss  15216  retopbas  15218  tgqioo  15250  dvexp  15406  efcn  15463  pilem3  15478