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Theorem sb9i 2542
Description: Commutation of quantification and substitution variables. Usage of this theorem is discouraged because it depends on ax-13 2382. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 15-Jun-2019.) (New usage is discouraged.)
Assertion
Ref Expression
sb9i (∀𝑥[𝑥 / 𝑦]𝜑 → ∀𝑦[𝑦 / 𝑥]𝜑)

Proof of Theorem sb9i
StepHypRef Expression
1 sb9 2541 . 2 (∀𝑥[𝑥 / 𝑦]𝜑 ↔ ∀𝑦[𝑦 / 𝑥]𝜑)
21biimpi 219 1 (∀𝑥[𝑥 / 𝑦]𝜑 → ∀𝑦[𝑦 / 𝑥]𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1536  [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  ax-10 2143  ax-11 2159  ax-12 2176  ax-13 2382
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070
This theorem is referenced by: (None)
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