Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Alan Sare
Virtual Deduction Theorems
e121
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
e121.1
⊢ ( 𝜑 ▶ 𝜓 )
e121.2
⊢ ( 𝜑 , 𝜒 ▶ 𝜃 )
e121.3
⊢ ( 𝜑 ▶ 𝜏 )
e121.4
⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion
e121
⊢ ( 𝜑 , 𝜒 ▶ 𝜂 )
Proof
Step
Hyp
Ref
Expression
1
e121.1
⊢ ( 𝜑 ▶ 𝜓 )
2
e121.2
⊢ ( 𝜑 , 𝜒 ▶ 𝜃 )
3
e121.3
⊢ ( 𝜑 ▶ 𝜏 )
4
e121.4
⊢ ( 𝜓 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5
1
vd12
⊢ ( 𝜑 , 𝜒 ▶ 𝜓 )
6
3
vd12
⊢ ( 𝜑 , 𝜒 ▶ 𝜏 )
7
5 2 6 4
e222
⊢ ( 𝜑 , 𝜒 ▶ 𝜂 )