New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  dveeq2 GIF version

Theorem dveeq2 1940
 Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.) (Revised by NM, 20-Jul-2015.)
Assertion
Ref Expression
dveeq2 x x = y → (z = yx z = y))
Distinct variable group:   x,z

Proof of Theorem dveeq2
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 equequ2 1686 . 2 (w = y → (z = wz = y))
21dvelimv 1939 1 x x = y → (z = yx z = y))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1540 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 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax10  1944  ax9  1949  ax11v2  1992  sbal1  2126  copsexg  4607
 Copyright terms: Public domain W3C validator