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Theorem equtrr 1683
Description: A transitive law for equality. Lemma L17 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtrr (x = y → (z = xz = y))

Proof of Theorem equtrr
StepHypRef Expression
1 equtr 1682 . 2 (z = x → (x = yz = y))
21com12 27 1 (x = y → (z = xz = y))
Colors of variables: wff setvar class
Syntax hints:  wi 4
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-ex 1542
This theorem is referenced by:  equtr2  1688  ax12b  1689  ax12bOLD  1690  ax12  1935  ax12from12o  2156  ax11eq  2193
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