Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Relations
xpeq2i
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xpeq12i
Metamath Proof Explorer
Ascii
Unicode
Theorem
xpeq2i
Description:
Equality inference for Cartesian product.
(Contributed by
NM
, 21-Dec-2008)
Ref
Expression
Hypothesis
xpeq1i.1
⊢
A
=
B
Assertion
xpeq2i
⊢
C
×
A
=
C
×
B
Proof
Step
Hyp
Ref
Expression
1
xpeq1i.1
⊢
A
=
B
2
xpeq2
⊢
A
=
B
→
C
×
A
=
C
×
B
3
1
2
ax-mp
⊢
C
×
A
=
C
×
B