Theorem simprld 771

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 497	. 2 ⊢ (𝜑 → (𝜒 ∧ 𝜃))
3	2	simpld 496	1 ⊢ (𝜑 → 𝜒)

Syntax hints:   → wi 4   ∧ wa 397

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 398

This theorem is referenced by:  fpwwe2lem5  10630  fpwwe2lem6  10631  fpwwe2lem8  10633  canthnumlem  10643  canthp1lem2  10648  latcl2  18389  clatlem  18455  dirtr  18555  srglz  20031  lmodvsass  20497  lmghm  20642  evlssca  21652  mircgr  27939  dfcgra2  28112  mgcmnt1d  32198  mgcmnt2d  32199  mgcf1o  32204  ssmxidllem  32620  ssmxidl  32621  maxsta  34576  lbioc  44274  icccncfext  44651  stoweidlem37  44801  fourierdlem41  44912  fourierdlem48  44918  fourierdlem49  44919  fourierdlem74  44944  fourierdlem75  44945  salgencl  45096  salgenuni  45101  issalgend  45102  smfaddlem1  45527