Theorem f1fun 6339

Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014.)

Assertion

Ref	Expression
f1fun	⊢ (𝐹:𝐴–1-1→𝐵 → Fun 𝐹)

Proof of Theorem f1fun

Step	Hyp	Ref	Expression
1		f1fn 6338	. 2 ⊢ (𝐹:𝐴–1-1→𝐵 → 𝐹 Fn 𝐴)
2		fnfun 6220	. 2 ⊢ (𝐹 Fn 𝐴 → Fun 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹:𝐴–1-1→𝐵 → Fun 𝐹)

Syntax hints:   → wi 4  Fun wfun 6116   Fn wfn 6117  –1-1→wf1 6119

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 199  df-an 387  df-fn 6125  df-f 6126  df-f1 6127

This theorem is referenced by:  f1cocnv2  6404  f1o2ndf1  7548  fnwelem  7555  f1dmvrnfibi  8518  fsuppco  8575  ackbij1b  9375  fin23lem31  9479  fin1a2lem6  9541  hashimarn  13515  gsumval3lem1  18658  gsumval3lem2  18659  usgrfun  26456  trlsegvdeglem6  27601  elhf  32819