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Theorem equsb3lem 2429
 Description: Lemma for equsb3 2430. (Contributed by Raph Levien and FL, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.)
Assertion
Ref Expression
equsb3lem ([𝑥 / 𝑦]𝑦 = 𝑧𝑥 = 𝑧)
Distinct variable groups:   𝑦,𝑧   𝑥,𝑦

Proof of Theorem equsb3lem
StepHypRef Expression
1 nfv 1841 . 2 𝑦 𝑥 = 𝑧
2 equequ1 1950 . 2 (𝑦 = 𝑥 → (𝑦 = 𝑧𝑥 = 𝑧))
31, 2sbie 2406 1 ([𝑥 / 𝑦]𝑦 = 𝑧𝑥 = 𝑧)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196  [wsb 1878 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-10 2017  ax-12 2045  ax-13 2244 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1703  df-nf 1708  df-sb 1879 This theorem is referenced by:  equsb3  2430  equsb3ALT  2431
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