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Metamath Proof Explorer

Theorem e11

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

Ref Expression
Hypotheses e11.1 ⊢ (    𝜑    ▶    𝜓    )
e11.2 ⊢ (    𝜑    ▶    𝜒    )
e11.3 ⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
Assertion e11 (    𝜑    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e11.1 ⊢ (    𝜑    ▶    𝜓    )
2 e11.2 ⊢ (    𝜑    ▶    𝜒    )
3 e11.3 ⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
4 3 a1i ⊢ ( 𝜓 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
5 1 1 2 4 e111 ⊢ (    𝜑    ▶    𝜃    )