Theorem simprr3 1104

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

Assertion

Ref	Expression
simprr3	⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Proof of Theorem simprr3

Step	Hyp	Ref	Expression
1		simpr3 1062	. 2 ⊢ ((𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒)) → 𝜒)
2	1	adantl 481	1 ⊢ ((𝜏 ∧ (𝜃 ∧ (𝜑 ∧ 𝜓 ∧ 𝜒))) → 𝜒)

Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031

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 196  df-an 385  df-3an 1033

This theorem is referenced by:  el2xptp0  7103  icodiamlt  14022  psgnunilem2  17738  srgbinom  18368  psgndiflemA  19766  haust1  20966  cnhaus  20968  isreg2  20991  llynlly  21090  restnlly  21095  llyrest  21098  llyidm  21101  nllyidm  21102  cldllycmp  21108  txlly  21249  txnlly  21250  pthaus  21251  txhaus  21260  txkgen  21265  xkohaus  21266  xkococnlem  21272  cmetcaulem  22894  itg2add  23332  ulmdvlem3  23960  ax5seglem6  25614  wwlkextfun  26257  frg2woteqm  26586  conpcon  30471  cvmlift3lem2  30556  cvmlift3lem8  30562  ifscgr  31321  broutsideof3  31403  unblimceq0  31668  paddasslem10  34133  lhpexle2lem  34313  lhpexle3lem  34315  mpaaeu  36739  stoweidlem35  38928  stoweidlem56  38949  stoweidlem59  38952  fusgrfis  40549  wwlksnextfun  41104  umgr2wlkon  41157