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ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Relations
coeq12i
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coeq12d
Metamath Proof Explorer
Ascii
Unicode
Theorem
coeq12i
Description:
Equality inference for composition of two classes.
(Contributed by
FL
, 7-Jun-2012)
Ref
Expression
Hypotheses
coeq12i.1
⊢
A
=
B
coeq12i.2
⊢
C
=
D
Assertion
coeq12i
⊢
A
∘
C
=
B
∘
D
Proof
Step
Hyp
Ref
Expression
1
coeq12i.1
⊢
A
=
B
2
coeq12i.2
⊢
C
=
D
3
1
coeq1i
⊢
A
∘
C
=
B
∘
C
4
2
coeq2i
⊢
B
∘
C
=
B
∘
D
5
3
4
eqtri
⊢
A
∘
C
=
B
∘
D