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Theorem bj-sbimeh 9912
 Description: A strengthening of sbieh 1673 (same proof). (Contributed by BJ, 16-Dec-2019.)
Hypotheses
Ref Expression
bj-sbimeh.1 (𝜓 → ∀𝑥𝜓)
bj-sbimeh.2 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
bj-sbimeh ([𝑦 / 𝑥]𝜑𝜓)

Proof of Theorem bj-sbimeh
StepHypRef Expression
1 tru 1247 . . . 4
21hbth 1352 . . 3 (⊤ → ∀𝑥⊤)
3 bj-sbimeh.1 . . . 4 (𝜓 → ∀𝑥𝜓)
43a1i 9 . . 3 (⊤ → (𝜓 → ∀𝑥𝜓))
5 bj-sbimeh.2 . . . 4 (𝑥 = 𝑦 → (𝜑𝜓))
65a1i 9 . . 3 (⊤ → (𝑥 = 𝑦 → (𝜑𝜓)))
72, 4, 6bj-sbimedh 9911 . 2 (⊤ → ([𝑦 / 𝑥]𝜑𝜓))
87trud 1252 1 ([𝑦 / 𝑥]𝜑𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∀wal 1241  ⊤wtru 1244  [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-sb 1646 This theorem is referenced by:  bj-sbime  9913
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