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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 39856. Contributed by Alan Sare 31-Dec-2011. (Contributed by NM, 31-Dec-2011.) |
Ref | Expression |
---|---|
nfra2 | ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2941 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 3122 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfral 3126 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1879 ∀wral 3089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-13 2377 ax-ext 2777 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-tru 1657 df-ex 1876 df-nf 1880 df-cleq 2792 df-clel 2795 df-nfc 2930 df-ral 3094 |
This theorem is referenced by: ralcom2 3285 invdisj 4829 reusv3 5075 dedekind 10490 dedekindle 10491 mreexexd 16623 gsummatr01lem4 20791 ordtconnlem1 30486 bnj1379 31418 tratrb 39522 islptre 40595 sprsymrelfo 42546 |
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