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Theorem bj-sbime 9913
Description: A strengthening of sbie 1674 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbime.nf 𝑥𝜓
bj-sbime.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-sbime ([𝑦 / 𝑥]𝜑𝜓)

Proof of Theorem bj-sbime
StepHypRef Expression
1 bj-sbime.nf . . 3 𝑥𝜓
21nfri 1412 . 2 (𝜓 → ∀𝑥𝜓)
3 bj-sbime.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
42, 3bj-sbimeh 9912 1 ([𝑦 / 𝑥]𝜑𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wnf 1349  [wsb 1645
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646
This theorem is referenced by:  setindis  10092  bdsetindis  10094
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