![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > nfra2 | Structured version Visualization version GIF version |
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD 44170. Usage of this theorem is discouraged because it depends on ax-13 2363. Use the weaker nfra2w 3288 when possible. (Contributed by Alan Sare, 31-Dec-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nfra2 | ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2895 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 3273 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfral 3362 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1777 ∀wral 3053 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-10 2129 ax-11 2146 ax-12 2163 ax-13 2363 ax-ext 2695 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-tru 1536 df-ex 1774 df-nf 1778 df-cleq 2716 df-clel 2802 df-nfc 2877 df-ral 3054 |
This theorem is referenced by: ralcom2 3365 |
Copyright terms: Public domain | W3C validator |