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First-order logic
Adding ax-4
bj-nexdh2
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bj-hbxfrbi
Metamath Proof Explorer
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Theorem
bj-nexdh2
Description:
Uncurried (imported) form of
bj-nexdh
.
(Contributed by
BJ
, 6-May-2019)
Ref
Expression
Assertion
bj-nexdh2
⊢
∀
x
φ
→
¬
ψ
∧
χ
→
∀
x
φ
→
χ
→
¬
∃
x
ψ
Proof
Step
Hyp
Ref
Expression
1
bj-nexdh
⊢
∀
x
φ
→
¬
ψ
→
χ
→
∀
x
φ
→
χ
→
¬
∃
x
ψ
2
1
imp
⊢
∀
x
φ
→
¬
ψ
∧
χ
→
∀
x
φ
→
χ
→
¬
∃
x
ψ