Theorem f1of1 5286

Description: A one-to-one onto mapping is a one-to-one mapping. (Contributed by set.mm contributors, 12-Dec-2003.)

Assertion

Ref	Expression
f1of1	|- (F:A-1-1-onto->B -> F:A-1-1->B)

Proof of Theorem f1of1

Step	Hyp	Ref	Expression
1		df-f1o 4794	. 2 |- (F:A-1-1-onto->B <-> (F:A-1-1->B /\ F:A-onto->B))
2	1	simplbi 446	1 |- (F:A-1-1-onto->B -> F:A-1-1->B)

Syntax hints:   -> wi 4  -1-1->wf1 4778  -onto->wfo 4779  -1-1-onto->wf1o 4780

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 177  df-an 360  df-f1o 4794

This theorem is referenced by:  f1of  5287  isoini2  5498  f1oiso  5499  swapres  5512  enpw1  6062  enpw1pw  6075  ncdisjun  6136  dflec3  6221  nclenc  6222  lenc  6223