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Theorem simp3r3 1284
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r3 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜒)

Proof of Theorem simp3r3
StepHypRef Expression
1 simpr3 1197 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant3 1136 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 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:  hash7g  14525  nllyrest  23494  cdlemblem  39795  cdleme21  40339  cdleme22b  40343  cdleme40m  40469  cdlemg34  40714  cdlemk5u  40863  cdlemk6u  40864  cdlemk21N  40875  cdlemk20  40876  cdlemk26b-3  40907  cdlemk26-3  40908  cdlemk28-3  40910  cdlemky  40928  cdlemk11t  40948  cdlemkyyN  40964  dihmeetlem20N  41328  stoweidlem56  46071
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