Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Operations
oveq1
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oveq2
Metamath Proof Explorer
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Theorem
oveq1
Description:
Equality theorem for operation value.
(Contributed by
NM
, 28-Feb-1995)
Ref
Expression
Assertion
oveq1
⊢
A
=
B
→
A
F
C
=
B
F
C
Proof
Step
Hyp
Ref
Expression
1
opeq1
⊢
A
=
B
→
A
C
=
B
C
2
1
fveq2d
⊢
A
=
B
→
F
⁡
A
C
=
F
⁡
B
C
3
df-ov
⊢
A
F
C
=
F
⁡
A
C
4
df-ov
⊢
B
F
C
=
F
⁡
B
C
5
2
3
4
3eqtr4g
⊢
A
=
B
→
A
F
C
=
B
F
C