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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-exlimh | Structured version Visualization version GIF version |
Description: Closed form of close to exlimih 2133. (Contributed by BJ, 2-May-2019.) |
Ref | Expression |
---|---|
bj-exlimh | ⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exim 1751 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃𝑥𝜑 → ∃𝑥𝜓)) | |
2 | 1 | imim1d 80 | 1 ⊢ (∀𝑥(𝜑 → 𝜓) → ((∃𝑥𝜓 → 𝜒) → (∃𝑥𝜑 → 𝜒))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 ∃wex 1695 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 |
This theorem depends on definitions: df-bi 196 df-ex 1696 |
This theorem is referenced by: bj-exlimh2 31788 |
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