Theorem simplld 764

Description: Deduction form of simpll 763, eliminating a double conjunct. (Contributed by Glauco Siliprandi, 11-Dec-2019.)

Hypothesis

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

Assertion

Ref	Expression
simplld	⊢ (𝜑 → 𝜓)

Proof of Theorem simplld

Step	Hyp	Ref	Expression
1		simplld.1	. . 3 ⊢ (𝜑 → ((𝜓 ∧ 𝜒) ∧ 𝜃))
2	1	simpld 493	. 2 ⊢ (𝜑 → (𝜓 ∧ 𝜒))
3	2	simpld 493	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4   ∧ wa 394

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 395

This theorem is referenced by:  erinxp  8787  lejoin1  18341  lemeet1  18355  reldir  18556  gexdvdsi  19492  lmhmlmod1  20788  pi1cpbl  24791  oppne1  28259  trgcopyeulem  28323  dfcgra2  28348  subupgr  28811  3trlond  29693  3pthond  29695  3spthond  29697  grpolid  30036  mgcf1  32425  mgccole1  32427  mgcmnt1  32429  mgcmnt2  32430  mgcf1olem1  32438  mgcf1olem2  32439  mgcf1o  32440  mfsdisj  34839  linethru  35429  rngoablo  37079  fourierdlem37  45158  fourierdlem48  45168  fourierdlem93  45213  fourierdlem94  45214  fourierdlem104  45224  fourierdlem112  45232  fourierdlem113  45233  dmmeasal  45466  meaf  45467  meaiuninclem  45494  omef  45510  ome0  45511  omedm  45513  hspmbllem3  45642