Theorem simp2lr 1242

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)

Assertion

Ref	Expression
simp2lr	⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Proof of Theorem simp2lr

Step	Hyp	Ref	Expression
1		simplr 768	. 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜓)
2	1	3ad2ant2 1134	1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜓)

Syntax hints:   → wi 4   ∧ wa 395   ∧ w3a 1086

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 207  df-an 396  df-3an 1088

This theorem is referenced by:  fpr3g  8215  tfrlem5  8299  omeu  8500  expmordi  14071  4sqlem18  16871  vdwlem10  16899  mvrf1  21921  mdetuni0  22534  mdetmul  22536  tsmsxp  24068  ax5seglem3  28907  btwnconn1lem1  36120  btwnconn1lem3  36122  btwnconn1lem4  36123  btwnconn1lem5  36124  btwnconn1lem6  36125  btwnconn1lem7  36126  linethru  36186  lshpkrlem6  39153  athgt  39494  2llnjN  39605  dalaw  39924  cdlemb2  40079  4atexlemex6  40112  cdleme01N  40259  cdleme0ex2N  40262  cdleme7aa  40280  cdleme7e  40285  cdlemg33c0  40740  dihmeetlem3N  41343  pellex  42867