Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Function operation
ofeq
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ofreq
Metamath Proof Explorer
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Theorem
ofeq
Description:
Equality theorem for function operation.
(Contributed by
Mario Carneiro
, 20-Jul-2014)
Ref
Expression
Assertion
ofeq
⊢
R
=
S
→
∘
f
⁡
R
=
∘
f
⁡
S
Proof
Step
Hyp
Ref
Expression
1
id
⊢
R
=
S
→
R
=
S
2
1
ofeqd
⊢
R
=
S
→
∘
f
⁡
R
=
∘
f
⁡
S