Metamath Proof Explorer


Theorem uneq1d

Description: Deduction adding union to the right in a class equality. (Contributed by NM, 29-Mar-1998)

Ref Expression
Hypothesis uneq1d.1 φA=B
Assertion uneq1d φAC=BC

Proof

Step Hyp Ref Expression
1 uneq1d.1 φA=B
2 uneq1 A=BAC=BC
3 1 2 syl φAC=BC