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Theorem simp2r3 1380
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 1256 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜒)
213ad2ant2 1168 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 386  w3a 1111
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 199  df-an 387  df-3an 1113
This theorem is referenced by:  btwnconn1lem8  32735  btwnconn1lem9  32736  btwnconn1lem10  32737  btwnconn1lem11  32738  btwnconn1lem12  32739  cdlemj3  36893  jm2.27  38413  iunrelexpmin2  38840
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