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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-2exim | Structured version Visualization version GIF version |
Description: Closed form of 2eximi 1831. (Contributed by BJ, 6-May-2019.) |
Ref | Expression |
---|---|
bj-2exim | ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exim 1829 | . 2 ⊢ (∀𝑦(𝜑 → 𝜓) → (∃𝑦𝜑 → ∃𝑦𝜓)) | |
2 | 1 | aleximi 1827 | 1 ⊢ (∀𝑥∀𝑦(𝜑 → 𝜓) → (∃𝑥∃𝑦𝜑 → ∃𝑥∃𝑦𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1533 ∃wex 1774 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 |
This theorem depends on definitions: df-bi 207 df-ex 1775 |
This theorem is referenced by: (None) |
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