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Theorem sbid2 1861
Description: An identity law for substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypothesis
Ref Expression
sbid2.1 𝑥𝜑
Assertion
Ref Expression
sbid2 ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)

Proof of Theorem sbid2
StepHypRef Expression
1 sbid2.1 . . 3 𝑥𝜑
21nfri 1530 . 2 (𝜑 → ∀𝑥𝜑)
32sbid2h 1860 1 ([𝑦 / 𝑥][𝑥 / 𝑦]𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wb 105  wnf 1471  [wsb 1773
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545
This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774
This theorem is referenced by:  sbco4lem  2018
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