New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > iineq2dv | GIF version |
Description: Equality deduction for indexed intersection. (Contributed by NM, 3-Aug-2004.) |
Ref | Expression |
---|---|
iuneq2dv.1 | ⊢ ((φ ∧ x ∈ A) → B = C) |
Ref | Expression |
---|---|
iineq2dv | ⊢ (φ → ∩x ∈ A B = ∩x ∈ A C) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1619 | . 2 ⊢ Ⅎxφ | |
2 | iuneq2dv.1 | . 2 ⊢ ((φ ∧ x ∈ A) → B = C) | |
3 | 1, 2 | iineq2d 3989 | 1 ⊢ (φ → ∩x ∈ A B = ∩x ∈ A C) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 = wceq 1642 ∈ wcel 1710 ∩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-ral 2619 df-iin 3972 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |