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Theorem equsb1v 2109
Description: Substitution applied to an atomic wff. Version of equsb1 2509 with a disjoint variable condition, which neither requires ax-12 2175 nor ax-13 2379. (Contributed by NM, 10-May-1993.) (Revised by BJ, 11-Sep-2019.) Remove dependencies on axioms. (Revised by Wolf Lammen, 30-May-2023.) (Proof shortened by Steven Nguyen, 19-Jun-2023.) Revise df-sb 2070. (Revised by Steven Nguyen, 11-Jul-2023.) (Proof shortened by Steven Nguyen, 22-Jul-2023.)
Assertion
Ref Expression
equsb1v [𝑦 / 𝑥]𝑥 = 𝑦
Distinct variable group:   𝑥,𝑦

Proof of Theorem equsb1v
StepHypRef Expression
1 equid 2019 . 2 𝑦 = 𝑦
2 equsb3 2106 . 2 ([𝑦 / 𝑥]𝑥 = 𝑦𝑦 = 𝑦)
31, 2mpbir 234 1 [𝑦 / 𝑥]𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  [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
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070
This theorem is referenced by:  pm13.183  3606  exss  5320
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