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Metamath Proof Explorer

Theorem e10

Description: A virtual deduction elimination rule (see mpisyl ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e10.1 ⊢ (    𝜑    ▶    𝜓    )
e10.2 ⊢ 𝜒
e10.3 ⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
Assertion e10 (    𝜑    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e10.1 ⊢ (    𝜑    ▶    𝜓    )
2 e10.2 ⊢ 𝜒
3 e10.3 ⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
4 2 vd01 ⊢ (    𝜑    ▶    𝜒    )
5 1 4 3 e11 ⊢ (    𝜑    ▶    𝜃    )