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Mathbox for Richard Penner
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Additional work on conditional logical operator
ifpbiidcor
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ifpbicor
Metamath Proof Explorer
Ascii
Structured
Theorem
ifpbiidcor
Description:
Restatement of
biid
.
(Contributed by
RP
, 25-Apr-2020)
Ref
Expression
Assertion
ifpbiidcor
⊢
if- (
𝜑
,
𝜑
, ¬
𝜑
)
Proof
Step
Hyp
Ref
Expression
1
biid
⊢
(
𝜑
↔
𝜑
)
2
ifpdfbi
⊢
( (
𝜑
↔
𝜑
) ↔ if- (
𝜑
,
𝜑
, ¬
𝜑
) )
3
1
2
mpbi
⊢
if- (
𝜑
,
𝜑
, ¬
𝜑
)