Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Operations
oveq
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oveq1
Metamath Proof Explorer
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Theorem
oveq
Description:
Equality theorem for operation value.
(Contributed by
NM
, 28-Feb-1995)
Ref
Expression
Assertion
oveq
⊢
F
=
G
→
A
F
B
=
A
G
B
Proof
Step
Hyp
Ref
Expression
1
fveq1
⊢
F
=
G
→
F
⁡
A
B
=
G
⁡
A
B
2
df-ov
⊢
A
F
B
=
F
⁡
A
B
3
df-ov
⊢
A
G
B
=
G
⁡
A
B
4
1
2
3
3eqtr4g
⊢
F
=
G
→
A
F
B
=
A
G
B