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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 39913. 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 2968 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 3149 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfral 3153 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1884 ∀wral 3116 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1896 ax-4 1910 ax-5 2011 ax-6 2077 ax-7 2114 ax-9 2175 ax-10 2194 ax-11 2209 ax-12 2222 ax-13 2390 ax-ext 2802 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 881 df-tru 1662 df-ex 1881 df-nf 1885 df-cleq 2817 df-clel 2820 df-nfc 2957 df-ral 3121 |
This theorem is referenced by: ralcom2 3313 invdisj 4858 reusv3 5104 dedekind 10518 dedekindle 10519 mreexexd 16660 gsummatr01lem4 20832 ordtconnlem1 30514 bnj1379 31446 tratrb 39579 islptre 40645 sprsymrelfo 42593 |
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