Theorem simprrd

Description: Deduction form of simprr , eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		simprrd.1	⊢ ( 𝜑 → ( 𝜓 ∧ ( 𝜒 ∧ 𝜃 ) ) )
2	1	simprd	⊢ ( 𝜑 → ( 𝜒 ∧ 𝜃 ) )
3	2	simprd	⊢ ( 𝜑 → 𝜃 )