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Mirrors > Home > MPE Home > Th. List > Mathboxes > bj-exlimmpi | Structured version Visualization version GIF version |
Description: Lemma for bj-vtoclg1f1 34723 (an instance of this lemma is a version of bj-vtoclg1f1 34723 where 𝑥 and 𝑦 are identified). (Contributed by BJ, 30-Apr-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-exlimmpi.nf | ⊢ Ⅎ𝑥𝜓 |
bj-exlimmpi.maj | ⊢ (𝜒 → (𝜑 → 𝜓)) |
bj-exlimmpi.min | ⊢ 𝜑 |
Ref | Expression |
---|---|
bj-exlimmpi | ⊢ (∃𝑥𝜒 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-exlimmpi.nf | . 2 ⊢ Ⅎ𝑥𝜓 | |
2 | bj-exlimmpi.min | . . 3 ⊢ 𝜑 | |
3 | bj-exlimmpi.maj | . . 3 ⊢ (𝜒 → (𝜑 → 𝜓)) | |
4 | 2, 3 | mpi 20 | . 2 ⊢ (𝜒 → 𝜓) |
5 | 1, 4 | exlimi 2218 | 1 ⊢ (∃𝑥𝜒 → 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∃wex 1786 Ⅎwnf 1790 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1802 ax-4 1816 ax-5 1916 ax-6 1974 ax-7 2019 ax-12 2178 |
This theorem depends on definitions: df-bi 210 df-ex 1787 df-nf 1791 |
This theorem is referenced by: bj-vtoclg1f1 34723 bj-vtoclg1f 34724 bj-vtoclg1fv 34725 |
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