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SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alan Sare
Virtual Deduction Theorems
e020
Metamath Proof Explorer
Description: A virtual deduction elimination rule. (Contributed by Alan Sare , 24-Jun-2011) (Proof modification is discouraged.)
(New usage is discouraged.)
Ref
Expression
Hypotheses
e020.1
⊢ 𝜑
e020.2
⊢ ( 𝜓 , 𝜒 ▶ 𝜃 )
e020.3
⊢ 𝜏
e020.4
⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion
e020
⊢ ( 𝜓 , 𝜒 ▶ 𝜂 )
Proof
Step
Hyp
Ref
Expression
1
e020.1
⊢ 𝜑
2
e020.2
⊢ ( 𝜓 , 𝜒 ▶ 𝜃 )
3
e020.3
⊢ 𝜏
4
e020.4
⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5
1
vd02
⊢ ( 𝜓 , 𝜒 ▶ 𝜑 )
6
3
vd02
⊢ ( 𝜓 , 𝜒 ▶ 𝜏 )
7
5 2 6 4
e222
⊢ ( 𝜓 , 𝜒 ▶ 𝜂 )