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  27908  dfcgra2  28081  mgcmnt1d  32167  mgcmnt2d  32168  mgcf1o  32173  ssmxidllem  32589  ssmxidl  32590  maxsta  34545  lbioc  44226  icccncfext  44603  stoweidlem37  44753  fourierdlem41  44864  fourierdlem48  44870  fourierdlem49  44871  fourierdlem74  44896  fourierdlem75  44897  salgencl  45048  salgenuni  45053  issalgend  45054  smfaddlem1  45479