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Theorem sbtrt 2534
 Description: Partially closed form of sbtr 2535. Usage of this theorem is discouraged because it depends on ax-13 2379. (Contributed by BJ, 4-Jun-2019.) (New usage is discouraged.)
Hypothesis
Ref Expression
sbtrt.nf 𝑦𝜑
Assertion
Ref Expression
sbtrt (∀𝑦[𝑦 / 𝑥]𝜑𝜑)

Proof of Theorem sbtrt
StepHypRef Expression
1 stdpc4 2073 . 2 (∀𝑦[𝑦 / 𝑥]𝜑 → [𝑥 / 𝑦][𝑦 / 𝑥]𝜑)
2 sbtrt.nf . . 3 𝑦𝜑
32sbid2 2527 . 2 ([𝑥 / 𝑦][𝑦 / 𝑥]𝜑𝜑)
41, 3sylib 221 1 (∀𝑦[𝑦 / 𝑥]𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∀wal 1536  Ⅎwnf 1785  [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 2142  ax-12 2175  ax-13 2379 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070 This theorem is referenced by:  sbtr  2535
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