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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-hbsb3 | Structured version Visualization version GIF version |
Description: Shorter proof of hbsb3 2496. (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 33247 | . 2 ⊢ (∀𝑥(𝜑 → ∀𝑦𝜑) → ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑)) | |
2 | bj-hbsb3.1 | . 2 ⊢ (𝜑 → ∀𝑦𝜑) | |
3 | 1, 2 | mpg 1898 | 1 ⊢ ([𝑦 / 𝑥]𝜑 → ∀𝑥[𝑦 / 𝑥]𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1656 [wsb 2069 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-10 2194 ax-12 2222 ax-13 2391 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-ex 1881 df-nf 1885 df-sb 2070 |
This theorem is referenced by: (None) |
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