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Metamath Proof Explorer

Theorem e01an

Description: Conjunction form of e01 . (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e01an.1 ⊢ 𝜑
e01an.2 ⊢ (    𝜓    ▶    𝜒    )
e01an.3 ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
Assertion e01an (    𝜓    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e01an.1 ⊢ 𝜑
2 e01an.2 ⊢ (    𝜓    ▶    𝜒    )
3 e01an.3 ⊢ ( ( 𝜑 ∧ 𝜒 ) → 𝜃 )
4 3 ex ⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )
5 1 2 4 e01 ⊢ (    𝜓    ▶    𝜃    )