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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 2910 | . 2 ⊢ (⊤ → Ⅎ𝑥 𝐴 ∈ 𝐵) |
6 | 5 | mptru 1549 | 1 ⊢ Ⅎ𝑥 𝐴 ∈ 𝐵 |
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