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Theorem equtr2 1594
Description: A transitive law for equality. (Contributed by NM, 12-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
equtr2 ((x = z y = z) → x = y)

Proof of Theorem equtr2
StepHypRef Expression
1 equtrr 1593 . . 3 (z = y → (x = zx = y))
21equcoms 1591 . 2 (y = z → (x = zx = y))
32impcom 116 1 ((x = z y = z) → x = y)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  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:  mo23  1938  euequ1  1992
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