Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Abbreviated conjunction and disjunction of three wff's
simp3r
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simp11
Metamath Proof Explorer
Ascii
Structured
Theorem
simp3r
Description:
Simplification of triple conjunction.
(Contributed by
NM
, 9-Nov-2011)
Ref
Expression
Assertion
simp3r
⊢
( (
𝜑
∧
𝜓
∧ (
𝜒
∧
𝜃
) ) →
𝜃
)
Proof
Step
Hyp
Ref
Expression
1
simpr
⊢
( (
𝜒
∧
𝜃
) →
𝜃
)
2
1
3ad2ant3
⊢
( (
𝜑
∧
𝜓
∧ (
𝜒
∧
𝜃
) ) →
𝜃
)