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Theorem sbid2v 2445
 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 1830 . 2 𝑥𝜑
21sbid2 2401 1 ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 195  [wsb 1867 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-12 2034  ax-13 2234 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868 This theorem is referenced by:  sbelx  2446  sbco4lem  2453
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