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Metamath Proof Explorer

Theorem e02an

Description: Conjunction form of e02 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e02an.1 ⊢ 𝜑
e02an.2 ⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
e02an.3 ⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
Assertion e02an (    𝜓    ,    𝜒    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e02an.1 ⊢ 𝜑
2 e02an.2 ⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3 e02an.3 ⊢ ( ( 𝜑 ∧ 𝜃 ) → 𝜏 )
4 3 ex ⊢ ( 𝜑 → ( 𝜃 → 𝜏 ) )
5 1 2 4 e02 ⊢ (    𝜓    ,    𝜒    ▶    𝜏    )