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Theorem pm13.193 38929
Description: Theorem *13.193 in [WhiteheadRussell] p. 179. (Contributed by Andrew Salmon, 3-Jun-2011.)
Assertion
Ref Expression
pm13.193 ((𝜑𝑥 = 𝑦) ↔ ([𝑦 / 𝑥]𝜑𝑥 = 𝑦))

Proof of Theorem pm13.193
StepHypRef Expression
1 sbequ12 2149 . 2 (𝑥 = 𝑦 → (𝜑 ↔ [𝑦 / 𝑥]𝜑))
21pm5.32ri 671 1 ((𝜑𝑥 = 𝑦) ↔ ([𝑦 / 𝑥]𝜑𝑥 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  wb 196  wa 383  [wsb 1937
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745  df-sb 1938
This theorem is referenced by: (None)
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