Theorem simprrd 538

Description: Deduction form of simprr 537, eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

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

Assertion

Ref	Expression
simprrd	⊢ (𝜑 → 𝜃)

Proof of Theorem simprrd

Step	Hyp	Ref	Expression
1		simprrd.1	. . 3 ⊢ (𝜑 → (𝜓 ∧ (𝜒 ∧ 𝜃)))
2	1	simprd 114	. 2 ⊢ (𝜑 → (𝜒 ∧ 𝜃))
3	2	simprd 114	1 ⊢ (𝜑 → 𝜃)

This proof depends on syntax axioms:   → wi 4   ∧ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107

This theorem is used by:  papcotr  7613  srgrz  14290  lmodvs1  14655