Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
fveq1d
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fveq2i
Metamath Proof Explorer
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Theorem
fveq1d
Description:
Equality deduction for function value.
(Contributed by
NM
, 2-Sep-2003)
Ref
Expression
Hypothesis
fveq1d.1
⊢
φ
→
F
=
G
Assertion
fveq1d
⊢
φ
→
F
⁡
A
=
G
⁡
A
Proof
Step
Hyp
Ref
Expression
1
fveq1d.1
⊢
φ
→
F
=
G
2
fveq1
⊢
F
=
G
→
F
⁡
A
=
G
⁡
A
3
1
2
syl
⊢
φ
→
F
⁡
A
=
G
⁡
A