Database
CLASSICAL FIRST-ORDER LOGIC WITH EQUALITY
Propositional calculus
Logical conjunction
imp5g
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imp55
Metamath Proof Explorer
Ascii
Unicode
Theorem
imp5g
Description:
An importation inference.
(Contributed by
Jeff Hankins
, 7-Jul-2009)
Ref
Expression
Hypothesis
imp5.1
⊢
φ
→
ψ
→
χ
→
θ
→
τ
→
η
Assertion
imp5g
⊢
φ
∧
ψ
→
χ
∧
θ
∧
τ
→
η
Proof
Step
Hyp
Ref
Expression
1
imp5.1
⊢
φ
→
ψ
→
χ
→
θ
→
τ
→
η
2
1
imp4b
⊢
φ
∧
ψ
→
χ
∧
θ
→
τ
→
η
3
2
impd
⊢
φ
∧
ψ
→
χ
∧
θ
∧
τ
→
η