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Theorem equsb1 2499
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 2482 . 2 (∀𝑥(𝑥 = 𝑦𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2 id 22 . 2 (𝑥 = 𝑦𝑥 = 𝑦)
31, 2mpg 1896 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 2067
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-12 2220  ax-13 2389
This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1879  df-sb 2068
This theorem is referenced by:  sbequ8ALT  2538  sbie  2539  pm13.183  3563  exss  5154  frege54cor1b  39023  sb5ALT  39564  sb5ALTVD  39962
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