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Theorem sbtrt 2557
Description: Partially closed form of sbtr 2558. (Contributed by BJ, 4-Jun-2019.)
Hypothesis
Ref Expression
sbtrt.nf 𝑦𝜑
Assertion
Ref Expression
sbtrt (∀𝑦[𝑦 / 𝑥]𝜑𝜑)

Proof of Theorem sbtrt
StepHypRef Expression
1 stdpc4 2490 . 2 (∀𝑦[𝑦 / 𝑥]𝜑 → [𝑥 / 𝑦][𝑦 / 𝑥]𝜑)
2 sbtrt.nf . . 3 𝑦𝜑
32sbid2 2550 . 2 ([𝑥 / 𝑦][𝑦 / 𝑥]𝜑𝜑)
41, 3sylib 208 1 (∀𝑦[𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1630  wnf 1857  [wsb 2046
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196  ax-13 2391
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-sb 2047
This theorem is referenced by:  sbtr  2558
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