MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  simp322 Structured version   Visualization version   GIF version

Theorem simp322 1407
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp322 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)

Proof of Theorem simp322
StepHypRef Expression
1 simp22 1248 . 2 ((𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏) → 𝜓)
213ad2ant3 1128 1 ((𝜂𝜁 ∧ (𝜃 ∧ (𝜑𝜓𝜒) ∧ 𝜏)) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  w3a 1070
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 197  df-an 383  df-3an 1072
This theorem is referenced by:  dalemqnet  35453  dalemrot  35458  dath2  35538  cdleme18d  36097  cdleme20i  36119  cdleme20j  36120  cdleme20l2  36123  cdleme20l  36124  cdleme20m  36125  cdleme20  36126  cdleme21j  36138  cdleme22eALTN  36147  cdleme26eALTN  36163  cdlemk16a  36658  cdlemk12u-2N  36692  cdlemk21-2N  36693  cdlemk22  36695  cdlemk31  36698  cdlemk32  36699  cdlemk11ta  36731  cdlemk11tc  36747
  Copyright terms: Public domain W3C validator