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Theorem sbid2vw 2261
Description: Reverting substitution yields the original expression. Based on fewer axioms than sbid2v 2551, at the expense of an extra distinct variable condition. (Contributed by NM, 14-May-1993.) (Revised by Wolf Lammen, 5-Aug-2023.)
Assertion
Ref Expression
sbid2vw ([𝑡 / 𝑥][𝑥 / 𝑡]𝜑𝜑)
Distinct variable groups:   𝑥,𝑡   𝜑,𝑥
Allowed substitution hint:   𝜑(𝑡)

Proof of Theorem sbid2vw
StepHypRef Expression
1 sbequ12r 2255 . 2 (𝑥 = 𝑡 → ([𝑥 / 𝑡]𝜑𝜑))
21sbievw 2103 1 ([𝑡 / 𝑥][𝑥 / 𝑡]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 209  [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-12 2178
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070
This theorem is referenced by:  sbco4lem  2284  ichid  43907
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