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Theorem sbtrt 2550
Description: Partially closed form of sbtr 2551. (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 2064 . 2 (∀𝑦[𝑦 / 𝑥]𝜑 → [𝑥 / 𝑦][𝑦 / 𝑥]𝜑)
2 sbtrt.nf . . 3 𝑦𝜑
32sbid2 2543 . 2 ([𝑥 / 𝑦][𝑦 / 𝑥]𝜑𝜑)
41, 3sylib 219 1 (∀𝑦[𝑦 / 𝑥]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  wnf 1775  [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-10 2136  ax-12 2167  ax-13 2381
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-ex 1772  df-nf 1776  df-sb 2061
This theorem is referenced by:  sbtr  2551
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