Metamath Proof Explorer

Theorem uneq12d

Description: Equality deduction for the union of two classes. (Contributed by NM, 29-Sep-2004) (Proof shortened by Andrew Salmon, 26-Jun-2011)

Ref Expression
Hypotheses uneq1d.1 φ A = B
uneq12d.2 φ C = D
Assertion uneq12d φ A C = B D


Step Hyp Ref Expression
1 uneq1d.1 φ A = B
2 uneq12d.2 φ C = D
3 uneq12 A = B C = D A C = B D
4 1 2 3 syl2anc φ A C = B D