![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > eximdv | GIF version |
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-1994.) |
Ref | Expression |
---|---|
alimdv.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
eximdv | ⊢ (φ → (∃xψ → ∃xχ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1416 | . 2 ⊢ (φ → ∀xφ) | |
2 | alimdv.1 | . 2 ⊢ (φ → (ψ → χ)) | |
3 | 1, 2 | eximdh 1499 | 1 ⊢ (φ → (∃xψ → ∃xχ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃wex 1378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-4 1397 ax-17 1416 ax-ial 1424 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: 2eximdv 1759 reximdv2 2412 cgsexg 2583 spc3egv 2638 euind 2722 ssel 2933 reupick 3215 reximdva0m 3230 uniss 3592 eusvnfb 4152 coss1 4434 coss2 4435 dmss 4477 dmcosseq 4546 funssres 4885 imain 4924 brprcneu 5114 fv3 5140 dffo4 5258 dffo5 5259 f1eqcocnv 5374 dmaddpq 6363 dmmulpq 6364 recexprlemlol 6598 recexprlemupu 6600 |
Copyright terms: Public domain | W3C validator |