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Theorem sbtrt 2517
Description: Partially closed form of sbtr 2518. Usage of this theorem is discouraged because it depends on ax-13 2370. (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 2070 . 2 (∀𝑦[𝑦 / 𝑥]𝜑 → [𝑥 / 𝑦][𝑦 / 𝑥]𝜑)
2 sbtrt.nf . . 3 𝑦𝜑
32sbid2 2510 . 2 ([𝑥 / 𝑦][𝑦 / 𝑥]𝜑𝜑)
41, 3sylib 217 1 (∀𝑦[𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1538  wnf 1784  [wsb 2066
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-10 2136  ax-12 2170  ax-13 2370
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-ex 1781  df-nf 1785  df-sb 2067
This theorem is referenced by:  sbtr  2518
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