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Theorem dveeq1 2018
Description: Quantifier introduction when one pair of variables is distinct. (Contributed by NM, 2-Jan-2002.)
Assertion
Ref Expression
dveeq1 x x = y → (y = zx y = z))
Distinct variable group:   x,z

Proof of Theorem dveeq1
Dummy variable w is distinct from all other variables.
StepHypRef Expression
1 equequ1 1684 . 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-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:  sbal2  2134
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