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Mirrors > Home > NFE Home > Th. List > nfii1 | GIF version |
Description: Bound-variable hypothesis builder for indexed intersection. (Contributed by NM, 15-Oct-2003.) |
Ref | Expression |
---|---|
nfii1 | ⊢ Ⅎx∩x ∈ A B |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iin 3972 | . 2 ⊢ ∩x ∈ A B = {y ∣ ∀x ∈ A y ∈ B} | |
2 | nfra1 2664 | . . 3 ⊢ Ⅎx∀x ∈ A y ∈ B | |
3 | 2 | nfab 2493 | . 2 ⊢ Ⅎx{y ∣ ∀x ∈ A y ∈ B} |
4 | 1, 3 | nfcxfr 2486 | 1 ⊢ Ⅎx∩x ∈ A B |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 1710 {cab 2339 Ⅎwnfc 2476 ∀wral 2614 ∩ciin 3970 |
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-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-iin 3972 |
This theorem is referenced by: dmiin 4965 |
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