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Metamath Proof Explorer

Theorem e03an

Description: Conjunction form of e03 . (Contributed by Alan Sare, 12-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e03an.1 ⊢ 𝜑
e03an.2 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
e03an.3 ⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
Assertion e03an (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )

Proof

Step Hyp Ref Expression
1 e03an.1 ⊢ 𝜑
2 e03an.2 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜏    )
3 e03an.3 ⊢ ( ( 𝜑 ∧ 𝜏 ) → 𝜂 )
4 3 ex ⊢ ( 𝜑 → ( 𝜏 → 𝜂 ) )
5 1 2 4 e03 ⊢ (    𝜓    ,    𝜒    ,    𝜃    ▶    𝜂    )