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Theorem pm13.193 40620
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 2243 . 2 (𝑥 = 𝑦 → (𝜑 ↔ [𝑦 / 𝑥]𝜑))
21pm5.32ri 576 1 ((𝜑𝑥 = 𝑦) ↔ ([𝑦 / 𝑥]𝜑𝑥 = 𝑦))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wa 396  [wsb 2060
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061
This theorem is referenced by: (None)
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