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Theorem dveel2 1894
 Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
dveel2 x x = y → (z yx z y))
Distinct variable group:   x,z

Proof of Theorem dveel2
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 ax-17 1416 . 2 (z wx z w)
2 ax-17 1416 . 2 (z yw z y)
3 elequ2 1598 . 2 (w = y → (z wz y))
41, 2, 3dvelimf 1888 1 x x = y → (z yx z y))
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1240 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643 This theorem is referenced by: (None)
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