NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  dveel1 GIF version

Theorem dveel1 2019
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
dveel1 x x = y → (y zx y z))
Distinct variable group:   x,z

Proof of Theorem dveel1
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 elequ1 1713 . 2 (w = y → (w zy z))
21dvelimv 1939 1 x x = y → (y zx y z))
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-13 1712  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: (None)
  Copyright terms: Public domain W3C validator