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Metamath Proof Explorer

Theorem preq12

Description: Equality theorem for unordered pairs. (Contributed by NM, 19-Oct-2012)

Ref Expression
Assertion preq12 ⊢ A = C ∧ B = D → A B = C D

Proof

Step Hyp Ref Expression
1 preq1 ⊢ A = C → A B = C B
2 preq2 ⊢ B = D → C B = C D
3 1 2 sylan9eq ⊢ A = C ∧ B = D → A B = C D