![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 19.40 | GIF version |
Description: Theorem 19.40 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
19.40 | ⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exsimpl 1505 | . 2 ⊢ (∃x(φ ∧ ψ) → ∃xφ) | |
2 | simpr 103 | . . 3 ⊢ ((φ ∧ ψ) → ψ) | |
3 | 2 | eximi 1488 | . 2 ⊢ (∃x(φ ∧ ψ) → ∃xψ) |
4 | 1, 3 | jca 290 | 1 ⊢ (∃x(φ ∧ ψ) → (∃xφ ∧ ∃xψ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∃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-ial 1424 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: 19.40-2 1520 19.41h 1572 19.41 1573 exdistrfor 1678 uniin 3591 copsexg 3972 dmin 4486 imadif 4922 imainlem 4923 |
Copyright terms: Public domain | W3C validator |