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Theorem simp2r3 1361
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp2r3 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)

Proof of Theorem simp2r3
StepHypRef Expression
1 simpr3 1237 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant2 1128 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071
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 1073
This theorem is referenced by:  btwnconn1lem8  32538  btwnconn1lem9  32539  btwnconn1lem10  32540  btwnconn1lem11  32541  btwnconn1lem12  32542  cdlemj3  36632  jm2.27  38101  iunrelexpmin2  38530
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