| Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-2exim | Structured version Visualization version GIF version | ||
| Description: Closed form of 2eximi 1836. (Contributed by BJ, 6-May-2019.) |
| Ref | Expression |
|---|---|
| bj-2exim | ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓)) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | exim 1834 | . 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∃𝑦𝜑 → ∃𝑦𝜓)) | |
| 2 | 1 | aleximi 1832 | 1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓)) |
| Colors of variables: wff setvar class |
| Syntax hints: → wi 4 ∀wal 1538 ∃wex 1779 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 |
| This theorem depends on definitions: df-bi 207 df-ex 1780 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |