Theorem simp1rr 1238

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

Assertion

Ref	Expression
simp1rr	⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 𝜏) → 𝜓)

Proof of Theorem simp1rr

Step	Hyp	Ref	Expression
1		simprr 770	. 2 ⊢ ((𝜒 ∧ (𝜑 ∧ 𝜓)) → 𝜓)
2	1	3ad2ant1 1132	1 ⊢ (((𝜒 ∧ (𝜑 ∧ 𝜓)) ∧ 𝜃 ∧ 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 206  df-an 396  df-3an 1088

This theorem is referenced by:  f1imass  7266  smo11  8367  zsupss  12926  lsmcv  20900  lspsolvlem  20901  mat2pmatghm  22453  mat2pmatmul  22454  nrmr0reg  23474  plyadd  25967  plymul  25968  coeeu  25975  ax5seglem6  28460  archiabl  32615  mdetpmtr1  33102  sseqval  33686  wsuclem  35102  btwnconn1lem1  35364  btwnconn1lem2  35365  btwnconn1lem12  35375  lshpsmreu  38283  1cvratlt  38649  llnle  38693  lvolex3N  38713  lnjatN  38955  lncvrat  38957  lncmp  38958  cdlemd6  39378  cdlemk19ylem  40105  pellex  41876  tfsconcatrn  42395  limcperiod  44643  itschlc0xyqsol1  47540  itschlc0xyqsol  47541