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Theorem ninjust 3210
 Description: Soundness theorem for df-nin 3211. (Contributed by SF, 10-Jan-2015.)
Assertion
Ref Expression
ninjust {x (x A x B)} = {y (y A y B)}
Distinct variable groups:   x,A,y   x,B,y

Proof of Theorem ninjust
StepHypRef Expression
1 eleq1 2413 . . 3 (x = y → (x Ay A))
2 eleq1 2413 . . 3 (x = y → (x By B))
31, 2nanbi12d 1303 . 2 (x = y → ((x A x B) ↔ (y A y B)))
43cbvabv 2472 1 {x (x A x B)} = {y (y A y B)}
 Colors of variables: wff setvar class Syntax hints:   ⊼ wnan 1287   = wceq 1642   ∈ 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-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349 This theorem is referenced by: (None)
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