 New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  isof1o GIF version

Theorem isof1o 5488
 Description: An isomorphism is a one-to-one onto function. (Contributed by set.mm contributors, 27-Apr-2004.)
Assertion
Ref Expression
isof1o (H Isom R, S (A, B) → H:A1-1-ontoB)

Proof of Theorem isof1o
Dummy variables x y are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-iso 4796 . 2 (H Isom R, S (A, B) ↔ (H:A1-1-ontoB x A y A (xRy ↔ (Hx)S(Hy))))
21simplbi 446 1 (H Isom R, S (A, B) → H:A1-1-ontoB)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176  ∀wral 2614   class class class wbr 4639  –1-1-onto→wf1o 4780   ‘cfv 4781   Isom wiso 4782 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360  df-iso 4796 This theorem is referenced by:  isomin  5496  isoini  5497  isoini2  5498
 Copyright terms: Public domain W3C validator