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Theorem equsb2 1710
Description: Substitution applied to an atomic wff. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
equsb2 [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2
StepHypRef Expression
1 sb2 1691 . 2 (∀𝑥(𝑥 = 𝑦𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2 equcomi 1633 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2mpg 1381 1 [𝑦 / 𝑥]𝑦 = 𝑥
Colors of variables: wff set class
Syntax hints:  wi 4  [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1687
This theorem is referenced by:  sbco  1884
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