Theorem f1orel 6053

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 6052	. 2 ⊢ (𝐹:𝐴–1-1-onto→𝐵 → Fun 𝐹)
2		funrel 5821	. 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 5043  Fun wfun 5798  –1-1-onto→wf1o 5803

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 196  df-an 385  df-fun 5806  df-fn 5807  df-f 5808  df-f1 5809  df-f1o 5811

This theorem is referenced by:  f1ococnv1  6078  isores1  6484  weisoeq2  6506  f1oexrnex  7008  ssenen  8019  cantnffval2  8475  hasheqf1oi  13002  hasheqf1oiOLD  13003  cmphaushmeo  21413  poimirlem3  32582  f1ocan2fv  32692  ltrncnvnid  34431  brco2f1o  37350  brco3f1o  37351  ntrclsnvobr  37370  ntrclsiex  37371  ntrneiiex  37394  ntrneinex  37395  neicvgel1  37437