Theorem f1orel 6841

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003.)

Assertion

Ref	Expression
f1orel	⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹)

Proof of Theorem f1orel

Step	Hyp	Ref	Expression
1		f1ofun 6840	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹)
2		funrel 6571	. 2 ⊢ (Fun 𝐹 → Rel 𝐹)
3	1, 2	syl 17	1 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Rel 𝐹)

Syntax hints:   → wi 4  Rel wrel 5683  Fun wfun 6543  –1-1-onto→wf1o 6548

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 206  df-an 395  df-fun 6551  df-fn 6552  df-f 6553  df-f1 6554  df-f1o 6556

This theorem is referenced by:  f1ococnv1  6867  isores1  7341  weisoeq2  7363  f1oexrnex  7935  ssenen  9176  f1oenfirn  9208  cantnffval2  9720  hasheqf1oi  14346  cmphaushmeo  23748  cycpmconjs  32969  poimirlem3  37227  f1ocan2fv  37331  ltrncnvnid  39730  brco2f1o  43604  brco3f1o  43605  ntrclsnvobr  43624  ntrclsiex  43625  ntrneiiex  43648  ntrneinex  43649  neicvgel1  43691