|   | Mathbox for BJ | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-alrim2 | Structured version Visualization version GIF version | ||
| Description: Uncurried (imported) form of bj-alrim 36694. (Contributed by BJ, 2-May-2019.) | 
| Ref | Expression | 
|---|---|
| bj-alrim2 | ⊢ ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑 → 𝜓)) → (𝜑 → ∀𝑥𝜓)) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | bj-alrim 36694 | . 2 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) | |
| 2 | 1 | imp 406 | 1 ⊢ ((Ⅎ𝑥𝜑 ∧ ∀𝑥(𝜑 → 𝜓)) → (𝜑 → ∀𝑥𝜓)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∧ wa 395 ∀wal 1538 Ⅎwnf 1783 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-12 2177 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-ex 1780 df-nf 1784 | 
| This theorem is referenced by: (None) | 
| Copyright terms: Public domain | W3C validator |