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Theorem equtr 1639
Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)
Assertion
Ref Expression
equtr (𝑥 = 𝑦 → (𝑦 = 𝑧𝑥 = 𝑧))

Proof of Theorem equtr
StepHypRef Expression
1 ax-8 1438 . 2 (𝑦 = 𝑥 → (𝑦 = 𝑧𝑥 = 𝑧))
21equcoms 1638 1 (𝑥 = 𝑦 → (𝑦 = 𝑧𝑥 = 𝑧))
Colors of variables: wff set class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-gen 1381  ax-ie2 1426  ax-8 1438  ax-17 1462  ax-i9 1466
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  equtrr  1640  equequ1  1642  equveli  1686  equvin  1788
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