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Mirrors > Home > ILE Home > Th. List > exlimd | GIF version |
Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.) |
Ref | Expression |
---|---|
exlimd.1 | ⊢ Ⅎ𝑥𝜑 |
exlimd.2 | ⊢ Ⅎ𝑥𝜒 |
exlimd.3 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
exlimd | ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exlimd.1 | . . 3 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | nfri 1412 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | exlimd.2 | . . 3 ⊢ Ⅎ𝑥𝜒 | |
4 | 3 | nfri 1412 | . 2 ⊢ (𝜒 → ∀𝑥𝜒) |
5 | exlimd.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
6 | 2, 4, 5 | exlimdh 1487 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1349 ∃wex 1381 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-5 1336 ax-gen 1338 ax-ie2 1383 ax-4 1400 |
This theorem depends on definitions: df-bi 110 df-nf 1350 |
This theorem is referenced by: exlimdd 1752 ceqsalg 2582 copsex2t 3982 alxfr 4193 mosubopt 4405 ovmpt2df 5632 ovi3 5637 bj-exlimmp 9909 |
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