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Theorem simpl33 1257
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) (Proof shortened by Wolf Lammen, 24-Jun-2022.)
Assertion
Ref Expression
simpl33 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)

Proof of Theorem simpl33
StepHypRef Expression
1 simpl3 1194 . 2 (((𝜑𝜓𝜒) ∧ 𝜂) → 𝜒)
213ad2antl3 1188 1 (((𝜃𝜏 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1087
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 1089
This theorem is referenced by:  nosupres  27752  noinfres  27767  ax5seglem3a  28945  ax5seg  28953  numclwwlk1lem2foa  30373  br8d  32622  br8  35756  cgrextend  36009  segconeq  36011  trisegint  36029  ifscgr  36045  cgrsub  36046  btwnxfr  36057  seglecgr12im  36111  segletr  36115  atbtwn  39448  4atlem10b  39607  4atlem11  39611  4atlem12  39614  2lplnj  39622  paddasslem4  39825  paddasslem7  39828  pmodlem1  39848  4atex2  40079  trlval3  40189  arglem1N  40192  cdleme0moN  40227  cdleme20  40326  cdleme21j  40338  cdleme28c  40374  cdleme38n  40466  cdlemg6c  40622  cdlemg6  40625  cdlemg7N  40628  cdlemg16  40659  cdlemg16ALTN  40660  cdlemg16zz  40662  cdlemg20  40687  cdlemg22  40689  cdlemg37  40691  cdlemg31d  40702  cdlemg29  40707  cdlemg33b  40709  cdlemg33  40713  cdlemg46  40737  cdlemk25-3  40906
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