Theorem e20an 42355

Description: Conjunction form of e20 42354. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
e20an.1	⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
e20an.2	⊢ 𝜃
e20an.3	⊢ ((𝜒 ∧ 𝜃) → 𝜏)

Assertion

Ref	Expression
e20an	⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Proof of Theorem e20an

Step	Hyp	Ref	Expression
1		e20an.1	. 2 ⊢ (   𝜑   ,   𝜓   ▶   𝜒   )
2		e20an.2	. 2 ⊢ 𝜃
3		e20an.3	. . 3 ⊢ ((𝜒 ∧ 𝜃) → 𝜏)
4	3	ex 413	. 2 ⊢ (𝜒 → (𝜃 → 𝜏))
5	1, 2, 4	e20 42354	1 ⊢ (   𝜑   ,   𝜓   ▶   𝜏   )

Syntax hints:   → wi 4   ∧ wa 396  (   wvd2 42204

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-vd2 42205

This theorem is referenced by: (None)