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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 44299. Usage of this theorem is discouraged because it depends on ax-13 2367. Use the weaker nfra2w 3293 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 2899 | . 2 ⊢ Ⅎ𝑦𝐴 | |
2 | nfra1 3278 | . 2 ⊢ Ⅎ𝑦∀𝑦 ∈ 𝐵 𝜑 | |
3 | 1, 2 | nfral 3367 | 1 ⊢ Ⅎ𝑦∀𝑥 ∈ 𝐴 ∀𝑦 ∈ 𝐵 𝜑 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1778 ∀wral 3058 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-13 2367 ax-ext 2699 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-tru 1537 df-ex 1775 df-nf 1779 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ral 3059 |
This theorem is referenced by: ralcom2 3370 |
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