Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Abbreviated conjunction and disjunction of three wff's
simp323
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simp331
Metamath Proof Explorer
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Theorem
simp323
Description:
Simplification of conjunction.
(Contributed by
NM
, 9-Mar-2012)
Ref
Expression
Assertion
simp323
⊢
η
∧
ζ
∧
θ
∧
φ
∧
ψ
∧
χ
∧
τ
→
χ
Proof
Step
Hyp
Ref
Expression
1
simp23
⊢
θ
∧
φ
∧
ψ
∧
χ
∧
τ
→
χ
2
1
3ad2ant3
⊢
η
∧
ζ
∧
θ
∧
φ
∧
ψ
∧
χ
∧
τ
→
χ