Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Functions
fneq2i
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nffn
Metamath Proof Explorer
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Theorem
fneq2i
Description:
Equality inference for function predicate with domain.
(Contributed by
NM
, 4-Sep-2011)
Ref
Expression
Hypothesis
fneq2i.1
⊢
A
=
B
Assertion
fneq2i
⊢
F
Fn
A
↔
F
Fn
B
Proof
Step
Hyp
Ref
Expression
1
fneq2i.1
⊢
A
=
B
2
fneq2
⊢
A
=
B
→
F
Fn
A
↔
F
Fn
B
3
1
2
ax-mp
⊢
F
Fn
A
↔
F
Fn
B