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Theorem equtrr 2119
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 2118 . 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 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875
This theorem is referenced by:  equeuclr  2120  equequ2  2123  equvinvOLD  2128  equvelvOLD  2131  ax12v2  2213  2ax6elem  2541  wl-spae  33756  wl-ax8clv2  33828  ax12eq  34920  ax6e2eq  39461  ax6e2eqVD  39821
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