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Theorem equtrr 2068
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 2067 . 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 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1818
This theorem is referenced by:  equeuclr  2069  equequ2  2072  equvinv  2076  equvelv  2078  ax12v2  2162  2ax6elem  2550  wl-spae  33538  wl-ax8clv2  33613  ax12eq  34647  sbeqalbi  39020  ax6e2eq  39192  ax6e2eqVD  39559
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