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Theorem equequ1 1595
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 1392 . 2 (x = y → (x = zy = z))
2 equtr 1592 . 2 (x = y → (y = zx = z))
31, 2impbid 120 1 (x = y → (x = zy = z))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equveli  1639  drsb1  1677  equsb3lem  1821  euequ1  1992  axext3  2020  reu6  2724  reu7  2730  cbviota  4815  dff13f  5352  poxp  5794
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