Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alan Sare
Virtual Deduction Theorems
e122
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
e122.1
⊢ ( 𝜑 ▶ 𝜓 )
e122.2
⊢ ( 𝜑 , 𝜒 ▶ 𝜃 )
e122.3
⊢ ( 𝜑 , 𝜒 ▶ 𝜏 )
e122.4
⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion
e122
⊢ ( 𝜑 , 𝜒 ▶ 𝜂 )
Proof
Step
Hyp
Ref
Expression
1
e122.1
⊢ ( 𝜑 ▶ 𝜓 )
2
e122.2
⊢ ( 𝜑 , 𝜒 ▶ 𝜃 )
3
e122.3
⊢ ( 𝜑 , 𝜒 ▶ 𝜏 )
4
e122.4
⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5
1
vd12
⊢ ( 𝜑 , 𝜒 ▶ 𝜓 )
6
5 2 3 4
e222
⊢ ( 𝜑 , 𝜒 ▶ 𝜂 )