Theorem f1of1 5287

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 4795	. 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 4779  -onto->wfo 4780  -1-1-onto->wf1o 4781

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 4795

This theorem is referenced by:  f1of  5288  isoini2  5499  f1oiso  5500  swapres  5513  enpw1  6063  enpw1pw  6076  ncdisjun  6137  dflec3  6222  nclenc  6223  lenc  6224