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Theorem sbid2v 1914
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 ax-17 1460 . 2 (𝜑 → ∀𝑥𝜑)
21sbid2h 1771 1 ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 103  [wsb 1686
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-sb 1687
This theorem is referenced by:  bdph  10799
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