Theorem e12an

Description: Conjunction form of e12 (see syl6an ). (Contributed by Alan Sare, 11-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e12an.1	⊢ (    𝜑    ▶    𝜓    )
	e12an.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
	e12an.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
Assertion	e12an	⊢ (    𝜑    ,    𝜒    ▶    𝜏    )

Proof

Step	Hyp	Ref	Expression
1		e12an.1	⊢ (    𝜑    ▶    𝜓    )
2		e12an.2	⊢ (    𝜑    ,    𝜒    ▶    𝜃    )
3		e12an.3	⊢ ( ( 𝜓 ∧ 𝜃 ) → 𝜏 )
4	3	ex	⊢ ( 𝜓 → ( 𝜃 → 𝜏 ) )
5	1 2 4	e12	⊢ (    𝜑    ,    𝜒    ▶    𝜏    )