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Mirrors > Home > MPE Home > Th. List > Mathboxes > stdpc5t | Structured version Visualization version GIF version |
Description: Closed form of stdpc5 2198. (Possible to place it before 19.21t 2196 and use it to prove 19.21t 2196). (Contributed by BJ, 15-Sep-2018.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
stdpc5t | ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5r 2183 | . 2 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
2 | alim 1802 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∀𝑥𝜑 → ∀𝑥𝜓)) | |
3 | 1, 2 | syl9 77 | 1 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1526 Ⅎwnf 1775 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-12 2167 |
This theorem depends on definitions: df-bi 208 df-ex 1772 df-nf 1776 |
This theorem is referenced by: bj-stdpc5 34048 bj-19.21t0 34050 |
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