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Theorem equtr2 1688
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 1683 . . 3 (z = y → (x = zx = y))
21equcoms 1681 . 2 (y = z → (x = zx = y))
32impcom 419 1 ((x = z y = z) → x = y)
Colors of variables: wff setvar class
Syntax hints:  wi 4   wa 358
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
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542
This theorem is referenced by:  mo  2226  2mo  2282  euequ1  2292
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