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

Theorem vjust 2860
 Description: Soundness justification theorem for df-v 2861. (Contributed by Rodolfo Medina, 27-Apr-2010.)
Assertion
Ref Expression
vjust {x x = x} = {y y = y}

Proof of Theorem vjust
Dummy variable z is distinct from all other variables.
StepHypRef Expression
1 equid 1676 . . . . 5 x = x
21sbt 2033 . . . 4 [z / x]x = x
3 equid 1676 . . . . 5 y = y
43sbt 2033 . . . 4 [z / y]y = y
52, 42th 230 . . 3 ([z / x]x = x ↔ [z / y]y = y)
6 df-clab 2340 . . 3 (z {x x = x} ↔ [z / x]x = x)
7 df-clab 2340 . . 3 (z {y y = y} ↔ [z / y]y = y)
85, 6, 73bitr4i 268 . 2 (z {x x = x} ↔ z {y y = y})
98eqriv 2350 1 {x x = x} = {y y = y}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642  [wsb 1648   ∈ wcel 1710  {cab 2339 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator