![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > nfsab1 | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
nfsab1 | ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbab1 2760 | . 2 ⊢ (𝑦 ∈ {𝑥 ∣ 𝜑} → ∀𝑥 𝑦 ∈ {𝑥 ∣ 𝜑}) | |
2 | 1 | nf5i 2179 | 1 ⊢ Ⅎ𝑥 𝑦 ∈ {𝑥 ∣ 𝜑} |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1856 ∈ wcel 2145 {cab 2757 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1870 ax-4 1885 ax-5 1991 ax-6 2057 ax-7 2093 ax-10 2174 ax-12 2203 |
This theorem depends on definitions: df-bi 197 df-an 383 df-or 837 df-ex 1853 df-nf 1858 df-sb 2050 df-clab 2758 |
This theorem is referenced by: clelab 2897 nfab1 2915 ralab2 3523 rexab2 3525 eluniab 4585 elintab 4622 opabex3d 7292 opabex3 7293 setindtrs 38115 rababg 38402 |
Copyright terms: Public domain | W3C validator |