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Theorem sbid2v 2586
Description: An identity law for substitution. Used in proof of Theorem 9.7 of [Megill] p. 449 (p. 16 of the preprint). (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbid2v ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜑(𝑦)

Proof of Theorem sbid2v
StepHypRef Expression
1 nfv 1984 . 2 𝑥𝜑
21sbid2 2542 1 ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  [wsb 2038
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1863  ax-4 1878  ax-5 1980  ax-6 2046  ax-7 2082  ax-10 2160  ax-12 2188  ax-13 2383
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1846  df-nf 1851  df-sb 2039
This theorem is referenced by:  sbelx  2587  sbco4lem  2594
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