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Metamath Proof Explorer

Theorem e10an

Description: Conjunction form of e10 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e10an.1 ⊢ (    𝜑    ▶    𝜓    )
e10an.2 ⊢ 𝜒
e10an.3 ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion e10an (    𝜑    ▶    𝜃    )

Proof

Step Hyp Ref Expression
1 e10an.1 ⊢ (    𝜑    ▶    𝜓    )
2 e10an.2 ⊢ 𝜒
3 e10an.3 ⊢ ( ( 𝜓 ∧ 𝜒 ) → 𝜃 )
4 3 ex ⊢ ( 𝜓 → ( 𝜒 → 𝜃 ) )
5 1 2 4 e10 ⊢ (    𝜑    ▶    𝜃    )