Metamath Proof Explorer


Theorem e22an

Description: Conjunction form of e22 . (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses e22an.1 (    𝜑    ,    𝜓    ▶    𝜒    )
e22an.2 (    𝜑    ,    𝜓    ▶    𝜃    )
e22an.3 ( ( 𝜒𝜃 ) → 𝜏 )
Assertion e22an (    𝜑    ,    𝜓    ▶    𝜏    )

Proof

Step Hyp Ref Expression
1 e22an.1 (    𝜑    ,    𝜓    ▶    𝜒    )
2 e22an.2 (    𝜑    ,    𝜓    ▶    𝜃    )
3 e22an.3 ( ( 𝜒𝜃 ) → 𝜏 )
4 3 ex ( 𝜒 → ( 𝜃𝜏 ) )
5 1 2 4 e22 (    𝜑    ,    𝜓    ▶    𝜏    )