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Theorem equsb1 2514
Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.)
Assertion
Ref Expression
equsb1 [𝑦 / 𝑥]𝑥 = 𝑦

Proof of Theorem equsb1
StepHypRef Expression
1 sb2 2497 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2 id 22 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1871 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 2048
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-12 2202  ax-13 2407
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1852  df-sb 2049
This theorem is referenced by:  sbequ8ALT  2553  sbie  2554  pm13.183  3493  exss  5059  frege54cor1b  38707  sb5ALT  39250  sb5ALTVD  39665
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