Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  ifval Structured version   Unicode version

Theorem ifval 3948
 Description: Another expression of the value of the predicate, analogous to eqif 3947. See also the more specialized iftrue 3915 and iffalse 3918. (Contributed by BJ, 6-Apr-2019.)
Assertion
Ref Expression
ifval

Proof of Theorem ifval
StepHypRef Expression
1 eqif 3947 . 2
2 cases2 980 . 2
31, 2bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wa 370   wceq 1437  cif 3909 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-if 3910 This theorem is referenced by:  bj-projval  31545
 Copyright terms: Public domain W3C validator