Mathbox for Peter Mazsa |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > inex3 | Structured version Visualization version GIF version |
Description: More general sethood condition for the intersection relation. (Contributed by Peter Mazsa, 24-Nov-2019.) |
Ref | Expression |
---|---|
inex3 | ⊢ ((𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊) → (𝐴 ∩ 𝐵) ∈ V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | inex1g 4801 | . 2 ⊢ (𝐴 ∈ 𝑉 → (𝐴 ∩ 𝐵) ∈ V) | |
2 | inex2ALTV 34105 | . 2 ⊢ (𝐵 ∈ 𝑊 → (𝐴 ∩ 𝐵) ∈ V) | |
3 | 1, 2 | jaoi 394 | 1 ⊢ ((𝐴 ∈ 𝑉 ∨ 𝐵 ∈ 𝑊) → (𝐴 ∩ 𝐵) ∈ V) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 383 ∈ wcel 1990 Vcvv 3200 ∩ cin 3573 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-in 3581 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |