Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical conjunction
simprr
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simprrd
Metamath Proof Explorer
Ascii
Structured
Theorem
simprr
Description:
Simplification of a conjunction.
(Contributed by
NM
, 21-Mar-2007)
Ref
Expression
Assertion
simprr
⊢
( (
𝜑
∧ (
𝜓
∧
𝜒
) ) →
𝜒
)
Proof
Step
Hyp
Ref
Expression
1
id
⊢
(
𝜒
→
𝜒
)
2
1
ad2antll
⊢
( (
𝜑
∧ (
𝜓
∧
𝜒
) ) →
𝜒
)