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

Theorem ifex 3720
 Description: Conditional operator existence. (Contributed by NM, 2-Sep-2004.)
Hypotheses
Ref Expression
dedex.1 A V
dedex.2 B V
Assertion
Ref Expression
ifex if(φ, A, B) V

Proof of Theorem ifex
StepHypRef Expression
1 dedex.1 . 2 A V
2 dedex.2 . 2 B V
31, 2keepel 3719 1 if(φ, A, B) V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   ifcif 3662 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-if 3663 This theorem is referenced by:  ifexg  3721  setswithex  4322  tfinex  4485  enprmaplem5  6080
 Copyright terms: Public domain W3C validator