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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 1530 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) |
3 | exlimd.2 | . . 3 ⊢ Ⅎ𝑥𝜒 | |
4 | 3 | nfri 1530 | . 2 ⊢ (𝜒 → ∀𝑥𝜒) |
5 | exlimd.3 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
6 | 2, 4, 5 | exlimdh 1607 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → 𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1471 ∃wex 1503 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-5 1458 ax-gen 1460 ax-ie2 1505 ax-4 1521 |
This theorem depends on definitions: df-bi 117 df-nf 1472 |
This theorem is referenced by: exlimdd 1883 ceqsalg 2780 copsex2t 4260 alxfr 4476 mosubopt 4706 ovmpodf 6023 ovi3 6028 fsum2dlemstep 11460 fprod2dlemstep 11648 lss1d 13660 bj-exlimmp 14918 |
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