Metamath Proof Explorer


Theorem preq1d

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

Ref Expression
Hypothesis preq1d.1 φ A = B
Assertion preq1d φ A C = B C

Proof

Step Hyp Ref Expression
1 preq1d.1 φ A = B
2 preq1 A = B A C = B C
3 1 2 syl φ A C = B C