Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Operations
oveq12
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oveq1i
Metamath Proof Explorer
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Theorem
oveq12
Description:
Equality theorem for operation value.
(Contributed by
NM
, 16-Jul-1995)
Ref
Expression
Assertion
oveq12
⊢
A
=
B
∧
C
=
D
→
A
F
C
=
B
F
D
Proof
Step
Hyp
Ref
Expression
1
oveq1
⊢
A
=
B
→
A
F
C
=
B
F
C
2
oveq2
⊢
C
=
D
→
B
F
C
=
B
F
D
3
1
2
sylan9eq
⊢
A
=
B
∧
C
=
D
→
A
F
C
=
B
F
D