Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > eximdh | GIF version |
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.) |
Ref | Expression |
---|---|
eximdh.1 | ⊢ (𝜑 → ∀𝑥𝜑) |
eximdh.2 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
eximdh | ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eximdh.1 | . . 3 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | eximdh.2 | . . 3 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | alrimih 1445 | . 2 ⊢ (𝜑 → ∀𝑥(𝜓 → 𝜒)) |
4 | exim 1578 | . 2 ⊢ (∀𝑥(𝜓 → 𝜒) → (∃𝑥𝜓 → ∃𝑥𝜒)) | |
5 | 3, 4 | syl 14 | 1 ⊢ (𝜑 → (∃𝑥𝜓 → ∃𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1329 ∃wex 1468 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: eximd 1591 19.41h 1663 hbexd 1672 equsex 1706 equsexd 1707 spimeh 1717 sbiedh 1760 exdistrfor 1772 eximdv 1852 cbvexdh 1896 mopick2 2080 2euex 2084 bj-sbimedh 12967 |
Copyright terms: Public domain | W3C validator |