Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Abbreviated conjunction and disjunction of three wff's
3imp231
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3imp21
Metamath Proof Explorer
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Theorem
3imp231
Description:
Importation inference.
(Contributed by
Alan Sare
, 17-Oct-2017)
Ref
Expression
Hypothesis
3imp.1
⊢
φ
→
ψ
→
χ
→
θ
Assertion
3imp231
⊢
ψ
∧
χ
∧
φ
→
θ
Proof
Step
Hyp
Ref
Expression
1
3imp.1
⊢
φ
→
ψ
→
χ
→
θ
2
1
com3l
⊢
ψ
→
χ
→
φ
→
θ
3
2
3imp
⊢
ψ
∧
χ
∧
φ
→
θ