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Theorem equtrr 1995
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 1994 . 2 (𝑧 = 𝑥 → (𝑥 = 𝑦𝑧 = 𝑦))
21com12 32 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 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  equeuclr  1996  equequ2  1999  equvinv  2003  equvelv  2005  ax12v2  2089  2ax6elem  2477  wl-spae  33436  wl-ax8clv2  33511  ax12eq  34545  sbeqalbi  38918  ax6e2eq  39090  ax6e2eqVD  39457
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