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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-sbime | GIF version |
Description: A strengthening of sbie 1802 (same proof). (Contributed by BJ, 16-Dec-2019.) |
Ref | Expression |
---|---|
bj-sbime.nf | ⊢ Ⅎ𝑥𝜓 |
bj-sbime.1 | ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) |
Ref | Expression |
---|---|
bj-sbime | ⊢ ([𝑦 / 𝑥]𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-sbime.nf | . . 3 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | nfri 1530 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) |
3 | bj-sbime.1 | . 2 ⊢ (𝑥 = 𝑦 → (𝜑 → 𝜓)) | |
4 | 2, 3 | bj-sbimeh 14921 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 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-4 1521 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 |
This theorem is referenced by: setindis 15116 bdsetindis 15118 |
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