![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
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 1409 | . 2 ⊢ (ψ → ∀xψ) |
3 | exlimi.2 | . 2 ⊢ (φ → ψ) | |
4 | 2, 3 | exlimih 1481 | 1 ⊢ (∃xφ → ψ) |
Colors of variables: wff set class |
Syntax hints: → wi 4 Ⅎwnf 1346 ∃wex 1378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-gen 1335 ax-ie2 1380 ax-4 1397 |
This theorem depends on definitions: df-bi 110 df-nf 1347 |
This theorem is referenced by: 19.36i 1559 euexex 1982 ceqsex 2586 sbhypf 2597 vtoclgf 2606 vtoclef 2620 copsexg 3972 copsex2g 3974 ralxpf 4425 rexxpf 4426 dmcoss 4544 fv3 5140 tz6.12c 5146 0neqopab 5492 bj-exlimmpi 9245 |
Copyright terms: Public domain | W3C validator |