This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypothesis |
bnj1265.1 |
⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 ) |
|
Assertion |
bnj1265 |
⊢ ( 𝜑 → 𝜓 ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
bnj1265.1 |
⊢ ( 𝜑 → ∃ 𝑥 ∈ 𝐴 𝜓 ) |
| 2 |
1
|
bnj1196 |
⊢ ( 𝜑 → ∃ 𝑥 ( 𝑥 ∈ 𝐴 ∧ 𝜓 ) ) |
| 3 |
2
|
bnj1266 |
⊢ ( 𝜑 → ∃ 𝑥 𝜓 ) |
| 4 |
3
|
bnj937 |
⊢ ( 𝜑 → 𝜓 ) |