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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-sbfv | Structured version Visualization version GIF version |
Description: Version of sbf 2368 with a dv condition, which does not require ax-13 2234. (Contributed by BJ, 31-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-sbfv.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
bj-sbfv | ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-sbfv.1 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | bj-sbftv 31951 | . 2 ⊢ (Ⅎ𝑥𝜑 → ([𝑦 / 𝑥]𝜑 ↔ 𝜑)) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ([𝑦 / 𝑥]𝜑 ↔ 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 Ⅎwnf 1699 [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-12 2034 |
This theorem depends on definitions: df-bi 196 df-an 385 df-ex 1696 df-nf 1701 df-sb 1868 |
This theorem is referenced by: (None) |
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