Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The conditional operator for classes
ifex
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ifeqor
Metamath Proof Explorer
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Theorem
ifex
Description:
Existence of the conditional operator (inference form).
(Contributed by
NM
, 2-Sep-2004)
Ref
Expression
Hypotheses
ifex.1
⊢
A
∈
V
ifex.2
⊢
B
∈
V
Assertion
ifex
⊢
if
φ
A
B
∈
V
Proof
Step
Hyp
Ref
Expression
1
ifex.1
⊢
A
∈
V
2
ifex.2
⊢
B
∈
V
3
1
2
ifcli
⊢
if
φ
A
B
∈
V