Theorem simprld 791

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

Hypothesis

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

Assertion

Ref	Expression
simprld	⊢ (𝜑 → 𝜒)

Proof of Theorem simprld

Step	Hyp	Ref	Expression
1		simprld.1	. . 3 ⊢ (𝜑 → (𝜓 ∧ (𝜒 ∧ 𝜃)))
2	1	simprd 478	. 2 ⊢ (𝜑 → (𝜒 ∧ 𝜃))
3	2	simpld 474	1 ⊢ (𝜑 → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383

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 196  df-an 385

This theorem is referenced by:  evlssca  19343  dfcgra2  25521  lbioc  38586  icccncfext  38773  stoweidlem37  38930  fourierdlem41  39041  fourierdlem48  39047  fourierdlem49  39048  fourierdlem74  39073  fourierdlem75  39074  salgencl  39226  salgenuni  39231  issalgend  39232  smfaddlem1  39649