Theorem bnj707

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj707.1	⊢ ( 𝜒 → 𝜏 )
Assertion	bnj707	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )

Proof

Step	Hyp	Ref	Expression
1		bnj707.1	⊢ ( 𝜒 → 𝜏 )
2		bnj258	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) ↔ ( ( 𝜑 ∧ 𝜓 ∧ 𝜃 ) ∧ 𝜒 ) )
3	2	simprbi	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜒 )
4	3 1	syl	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ∧ 𝜃 ) → 𝜏 )