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Metamath Proof Explorer
Description: "At most one" exports disjunction to conjunction. (Contributed by NM, 5-Apr-2004) (Proof shortened by Andrew Salmon, 9-Jul-2011)
|
|
Ref |
Expression |
|
Assertion |
mooran2 |
⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ( ∃* 𝑥 𝜑 ∧ ∃* 𝑥 𝜓 ) ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
moor |
⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜑 ) |
| 2 |
|
olc |
⊢ ( 𝜓 → ( 𝜑 ∨ 𝜓 ) ) |
| 3 |
2
|
moimi |
⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ∃* 𝑥 𝜓 ) |
| 4 |
1 3
|
jca |
⊢ ( ∃* 𝑥 ( 𝜑 ∨ 𝜓 ) → ( ∃* 𝑥 𝜑 ∧ ∃* 𝑥 𝜓 ) ) |