Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-alrim | Structured version Visualization version GIF version |
Description: Closed form of alrimi 2082. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-alrim | ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nf5r 2064 | . 2 ⊢ (Ⅎ𝑥𝜑 → (𝜑 → ∀𝑥𝜑)) | |
2 | sylgt 1749 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → ((𝜑 → ∀𝑥𝜑) → (𝜑 → ∀𝑥𝜓))) | |
3 | 1, 2 | syl5com 31 | 1 ⊢ (Ⅎ𝑥𝜑 → (∀𝑥(𝜑 → 𝜓) → (𝜑 → ∀𝑥𝜓))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1481 Ⅎwnf 1708 |
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-12 2047 |
This theorem depends on definitions: df-bi 197 df-ex 1705 df-nf 1710 |
This theorem is referenced by: bj-alrim2 32684 |
Copyright terms: Public domain | W3C validator |