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Theorem equequ2 1596
Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equequ2 (x = y → (z = xz = y))

Proof of Theorem equequ2
StepHypRef Expression
1 equtrr 1593 . 2 (x = y → (z = xz = y))
2 equtrr 1593 . . 3 (y = x → (z = yz = x))
32equcoms 1591 . 2 (x = y → (z = yz = x))
41, 3impbid 120 1 (x = y → (z = xz = y))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
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-gen 1335  ax-ie2 1380  ax-8 1392  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  ax11v2  1698  ax11v  1705  ax11ev  1706  equs5or  1708  eujust  1899  euf  1902  mo23  1938  iotaval  4821  dffun4f  4861  dff13f  5352
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