Theorem simprrd 773

Description: Deduction form of simprr 772, 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 497	. 2 ⊢ (𝜑 → (𝜒 ∧ 𝜃))
3	2	simprd 497	1 ⊢ (𝜑 → 𝜃)

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:  fpwwe2lem3  10628  uzind  12654  latcl2  18389  clatlem  18455  dirge  18556  srgrz  20030  lmodvs1  20500  lmhmsca  20641  evlsvar  21653  mirbtwn  27909  dfcgra2  28081  3trlond  29426  3pthond  29428  3spthond  29430  ssmxidllem  32589  ssmxidl  32590  axtgupdim2ALTV  33680  mvtinf  34546  rngoid  36770  rngoideu  36771  rngorn1eq  36802  rngomndo  36803  fzne2d  40846  mzpcl34  41469  icccncfext  44603  fourierdlem12  44835  fourierdlem34  44857  fourierdlem41  44864  fourierdlem48  44870  fourierdlem49  44871  fourierdlem74  44896  fourierdlem75  44897  fourierdlem76  44898  fourierdlem89  44911  fourierdlem91  44913  fourierdlem92  44914  fourierdlem94  44916  fourierdlem113  44935  sssalgen  45051  issalgend  45054  smfaddlem1  45479