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## Proof: (related to "Justification of Set Union")

• Let $A$ and $B$ be sets.

• By the axiom of pairing there is a set $Z$ containing $A$ and $B$ as elements:

• By the axiom of union there is a set $Z^*$ containing the elements of $A$ or1 the elements of $B.$

• By the axiom of separation there is a subset $Z^\dagger \subseteq Z^*$ containing exactly the elements of $A$ or1 the elements of $B.$, i.e. $Z^\dagger =\{z\mid z\in A\vee z\in B\}.$

1 We mean the logical or operation, in the natural English language “and/or”.

q.e.d

| | | | created: 2019-01-12 22:41:54 | modified: 2019-01-12 22:44:47 | by: bookofproofs | references: [983]

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