Theorem fdmi 5275

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 5273	. 2 ⊢ (𝐹:𝐴⟶𝐵 → dom 𝐹 = 𝐴)
3	1, 2	ax-mp 5	1 ⊢ dom 𝐹 = 𝐴

Syntax hints:   = wceq 1331  dom cdm 4534  ⟶wf 5114

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 5121  df-f 5122

This theorem is referenced by:  suplocexprlemdisj  7521  suplocexprlemub  7524  eluzel2  9324  inftonninf  10207  qtopbasss  12679  retopbas  12681  tgqioo  12705  dvexp  12833  efcn  12846  pilem3  12853