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Theorem equequ1 1642
Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equequ1 (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))

Proof of Theorem equequ1
StepHypRef Expression
1 ax-8 1438 . 2 (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))
2 equtr 1639 . 2 (𝑥 = 𝑦 → (𝑦 = 𝑧𝑥 = 𝑧))
31, 2impbid 127 1 (𝑥 = 𝑦 → (𝑥 = 𝑧𝑦 = 𝑧))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  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:  equveli  1686  drsb1  1724  equsb3lem  1869  euequ1  2040  axext3  2068  reu6  2795  reu7  2801  cbviota  4953  dff13f  5512  poxp  5956  dcdifsnid  6219  supmoti  6635  isoti  6649
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