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Mirrors > Home > NFE Home > Th. List > uniiun | GIF version |
Description: Class union in terms of indexed union. Definition in [Stoll] p. 43. (Contributed by NM, 28-Jun-1998.) |
Ref | Expression |
---|---|
uniiun | ⊢ ∪A = ∪x ∈ A x |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfuni2 3893 | . 2 ⊢ ∪A = {y ∣ ∃x ∈ A y ∈ x} | |
2 | df-iun 3971 | . 2 ⊢ ∪x ∈ A x = {y ∣ ∃x ∈ A y ∈ x} | |
3 | 1, 2 | eqtr4i 2376 | 1 ⊢ ∪A = ∪x ∈ A x |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ∈ wcel 1710 {cab 2339 ∃wrex 2615 ∪cuni 3891 ∪ciun 3969 |
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-rex 2620 df-uni 3892 df-iun 3971 |
This theorem is referenced by: iununi 4050 iunpwss 4055 imauni 5465 |
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