Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The union of a class
unieqi
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unieqd
Metamath Proof Explorer
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Unicode
Theorem
unieqi
Description:
Inference of equality of two class unions.
(Contributed by
NM
, 30-Aug-1993)
Ref
Expression
Hypothesis
unieqi.1
⊢
A
=
B
Assertion
unieqi
⊢
⋃
A
=
⋃
B
Proof
Step
Hyp
Ref
Expression
1
unieqi.1
⊢
A
=
B
2
unieq
⊢
A
=
B
→
⋃
A
=
⋃
B
3
1
2
ax-mp
⊢
⋃
A
=
⋃
B