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Theorem equsb3lem 2101
Description: Lemma for equsb3 2102. (Contributed by Raph Levien and FL, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
equsb3lem ([y / x]x = zy = z)
Distinct variable groups:   x,z   x,y

Proof of Theorem equsb3lem
StepHypRef Expression
1 nfv 1619 . 2 x y = z
2 equequ1 1684 . 2 (x = y → (x = zy = z))
31, 2sbie 2038 1 ([y / x]x = zy = z)
Colors of variables: wff setvar class
Syntax hints:  wb 176  [wsb 1648
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649
This theorem is referenced by:  equsb3  2102
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