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Theorem equsb2 2510
 Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2379. Check out equsb1v 2109 for a version requiring less axioms. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)
Assertion
Ref Expression
equsb2 [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2
StepHypRef Expression
1 sb2 2493 . 2 (∀𝑥(𝑥 = 𝑦𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2 equcomi 2024 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2mpg 1799 1 [𝑦 / 𝑥]𝑦 = 𝑥
 Colors of variables: wff setvar class Syntax hints:   → wi 4  [wsb 2069 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-12 2175  ax-13 2379 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070 This theorem is referenced by:  bj-sbidmOLD  34604
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