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Mirrors > Home > ILE Home > Th. List > exlimi | GIF version |
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.) |
Ref | Expression |
---|---|
exlimi.1 | ⊢ Ⅎ𝑥𝜓 |
exlimi.2 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
exlimi | ⊢ (∃𝑥𝜑 → 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimi.1 | . . 3 ⊢ Ⅎ𝑥𝜓 | |
2 | 1 | nfri 1484 | . 2 ⊢ (𝜓 → ∀𝑥𝜓) |
3 | exlimi.2 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | 2, 3 | exlimih 1557 | 1 ⊢ (∃𝑥𝜑 → 𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1421 ∃wex 1453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-gen 1410 ax-ie2 1455 ax-4 1472 |
This theorem depends on definitions: df-bi 116 df-nf 1422 |
This theorem is referenced by: 19.36i 1635 euexex 2062 ceqsex 2698 sbhypf 2709 vtoclgf 2718 vtoclg1f 2719 vtoclef 2733 copsexg 4136 copsex2g 4138 ralxpf 4655 rexxpf 4656 dmcoss 4778 fv3 5412 tz6.12c 5419 0neqopab 5784 cnvoprab 6099 bj-exlimmpi 12904 |
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