Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alan Sare
Virtual Deduction Theorems
e202
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
e202.1
⊢ ( 𝜑 , 𝜓 ▶ 𝜒 )
e202.2
⊢ 𝜃
e202.3
⊢ ( 𝜑 , 𝜓 ▶ 𝜏 )
e202.4
⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion
e202
⊢ ( 𝜑 , 𝜓 ▶ 𝜂 )
Proof
Step
Hyp
Ref
Expression
1
e202.1
⊢ ( 𝜑 , 𝜓 ▶ 𝜒 )
2
e202.2
⊢ 𝜃
3
e202.3
⊢ ( 𝜑 , 𝜓 ▶ 𝜏 )
4
e202.4
⊢ ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5
2
vd02
⊢ ( 𝜑 , 𝜓 ▶ 𝜃 )
6
1 5 3 4
e222
⊢ ( 𝜑 , 𝜓 ▶ 𝜂 )