Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alan Sare
Virtual Deduction Theorems
e002
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
e002.1
⊢ 𝜑
e002.2
⊢ 𝜓
e002.3
⊢ ( 𝜒 , 𝜃 ▶ 𝜏 )
e002.4
⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
Assertion
e002
⊢ ( 𝜒 , 𝜃 ▶ 𝜂 )
Proof
Step
Hyp
Ref
Expression
1
e002.1
⊢ 𝜑
2
e002.2
⊢ 𝜓
3
e002.3
⊢ ( 𝜒 , 𝜃 ▶ 𝜏 )
4
e002.4
⊢ ( 𝜑 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) )
5
1
vd02
⊢ ( 𝜒 , 𝜃 ▶ 𝜑 )
6
2
vd02
⊢ ( 𝜒 , 𝜃 ▶ 𝜓 )
7
5 6 3 4
e222
⊢ ( 𝜒 , 𝜃 ▶ 𝜂 )