Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Operations
oveqd
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oveq12d
Metamath Proof Explorer
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Theorem
oveqd
Description:
Equality deduction for operation value.
(Contributed by
NM
, 9-Sep-2006)
Ref
Expression
Hypothesis
oveq1d.1
⊢
φ
→
A
=
B
Assertion
oveqd
⊢
φ
→
C
A
D
=
C
B
D
Proof
Step
Hyp
Ref
Expression
1
oveq1d.1
⊢
φ
→
A
=
B
2
oveq
⊢
A
=
B
→
C
A
D
=
C
B
D
3
1
2
syl
⊢
φ
→
C
A
D
=
C
B
D