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Theorem equsb1 2494
Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2375. Use the weaker equsb1v 2103 if possible. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)
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 1794 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wi 4  [wsb 2062
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-10 2139  ax-12 2175  ax-13 2375
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-ex 1777  df-nf 1781  df-sb 2063
This theorem is referenced by:  sbequ8  2504  sbie  2505  frege54cor1b  43884  sb5ALT  44523  sb5ALTVD  44911
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