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Mirrors > Home > NFE Home > Th. List > nfra2 | GIF version |
Description: Similar to Lemma 24 of [Monk2] p. 114, except the quantification of the antecedent is restricted. Derived automatically from hbra2VD in set.mm. 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 2489 | . 2 ⊢ ℲyA | |
2 | nfra1 2664 | . 2 ⊢ Ⅎy∀y ∈ B φ | |
3 | 1, 2 | nfral 2667 | 1 ⊢ Ⅎy∀x ∈ A ∀y ∈ B φ |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnf 1544 ∀wral 2614 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 |
This theorem is referenced by: ralcom2 2775 ncfinraise 4481 |
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