Metamath Proof Explorer


Theorem xrneq1d

Description: Equality theorem for the range Cartesian product, deduction form. (Contributed by Peter Mazsa, 7-Sep-2021)

Ref Expression
Hypothesis xrneq1d.1 φA=B
Assertion xrneq1d φAC=BC

Proof

Step Hyp Ref Expression
1 xrneq1d.1 φA=B
2 xrneq1 A=BAC=BC
3 1 2 syl φAC=BC