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 ( ( 𝜑𝜒 ) → 𝜃 )
Assertion e01an (    𝜓    ▶    𝜃    )

Proof

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