Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp33r Structured version   Visualization version   GIF version

Theorem simp33r 1182
 Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp33r ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simp33r
StepHypRef Expression
1 simp3r 1083 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜓)
213ad2ant3 1077 1 ((𝜏𝜂 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
 Colors of variables: wff setvar class 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:  totprob  29816  cdleme19b  34610  cdleme19e  34613  cdleme20h  34622  cdleme20l2  34627  cdleme20m  34629  cdleme21d  34636  cdleme21e  34637  cdleme22eALTN  34651  cdleme22f2  34653  cdleme22g  34654  cdleme26e  34665  cdleme37m  34768  cdlemeg46gfre  34838  cdlemg28a  34999  cdlemg28b  35009  cdlemk5a  35141  cdlemk6  35143
 Copyright terms: Public domain W3C validator