Theorem simp2l 930

Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.)

Assertion

Ref	Expression
simp2l	⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)

Proof of Theorem simp2l

Step	Hyp	Ref	Expression
1		simpl 102	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 926	1 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒) ∧ 𝜃) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 97   ∧ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  simpl2l  957  simpr2l  963  simp12l  1017  simp22l  1023  simp32l  1029  issod  4056  funprg  4949  fsnunf  5362  f1oiso2  5466  ecopovtrn  6203  ecopovtrng  6206  addassnqg  6480  ltsonq  6496  ltanqg  6498  ltmnqg  6499  addassnq0  6560  recexprlem1ssu  6732  mulasssrg  6843  distrsrg  6844  lttrsr  6847  ltsosr  6849  ltasrg  6855  mulextsr1lem  6864  mulextsr1  6865  axmulass  6947  axdistr  6948  dmdcanap  7698  ltdiv2  7853  lediv2  7857  ltdiv23  7858  lediv23  7859  expaddzaplem  9298  expaddzap  9299  expmulzap  9301  expdivap  9305