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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-hbsb3 | Structured version Visualization version GIF version |
Description: Shorter proof of hbsb3 2364. (Contributed by BJ, 2-May-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-hbsb3.1 | ⊢ (𝜑 → ∀𝑦𝜑) |
Ref | Expression |
---|---|
bj-hbsb3 | ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-hbsb3t 32712 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)) | |
2 | bj-hbsb3.1 | . 2 ⊢ (𝜑 → ∀𝑦𝜑) | |
3 | 1, 2 | mpg 1724 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 [wsb 1880 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-ex 1705 df-nf 1710 df-sb 1881 |
This theorem is referenced by: (None) |
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