| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > nfel | Structured version Visualization version GIF version | ||
| Description: Hypothesis builder for elementhood. (Contributed by NM, 1-Aug-1993.) (Revised by Mario Carneiro, 11-Aug-2016.) (Proof shortened by Wolf Lammen, 16-Nov-2019.) |
| Ref | Expression |
|---|---|
| nfnfc.1 | ⊢ Ⅎ𝑥𝐴 |
| nfeq.2 | ⊢ Ⅎ𝑥𝐵 |
| Ref | Expression |
|---|---|
| nfel | ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfnfc.1 | . . . 4 ⊢ Ⅎ𝑥𝐴 | |
| 2 | 1 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐴) |
| 3 | nfeq.2 | . . . 4 ⊢ Ⅎ𝑥𝐵 | |
| 4 | 3 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝐵) |
| 5 | 2, 4 | nfeld 2917 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴 ∈ 𝐵) |
| 6 | 5 | mptru 1547 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
| Copyright terms: Public domain | W3C validator |