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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-hbsb3v | Structured version Visualization version GIF version |
Description: Version of hbsb3 2352 with a dv condition, which does not require ax-13 2234. (Remark: the unbundled version of nfs1 2353 is given by bj-nfs1v 31947.) (Contributed by BJ, 11-Sep-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-hbsb3v.1 | ⊢ (𝜑 → ∀𝑦𝜑) |
Ref | Expression |
---|---|
bj-hbsb3v | ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbsb3v.1 | . . 3 ⊢ (𝜑 → ∀𝑦𝜑) | |
2 | 1 | sbimi 1873 | . 2 ⊢ ([𝑦 / 𝑥]𝜑 → [𝑦 / 𝑥]∀𝑦𝜑) |
3 | bj-hbsb2av 31948 | . 2 ⊢ ([𝑦 / 𝑥]∀𝑦𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) | |
4 | 2, 3 | syl 17 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 [wsb 1867 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 |
This theorem is referenced by: (None) |
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