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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-exlime | Structured version Visualization version GIF version |
Description: Variant of exlimih 2133 where the non-freeness of 𝑥 in 𝜓 is expressed using an existential quantifier. (Contributed by BJ, 17-Mar-2020.) |
Ref | Expression |
---|---|
bj-exlime.1 | ⊢ (∃𝑥𝜓 → 𝜓) |
bj-exlime.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
bj-exlime | ⊢ (∃𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-exlime.2 | . . 3 ⊢ (𝜑 → 𝜓) | |
2 | 1 | eximi 1752 | . 2 ⊢ (∃𝑥𝜑 → ∃𝑥𝜓) |
3 | bj-exlime.1 | . 2 ⊢ (∃𝑥𝜓 → 𝜓) | |
4 | 2, 3 | syl 17 | 1 ⊢ (∃𝑥𝜑 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃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-cbvexiw 31846 |
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