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Theorem simp2r1 1276
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp2r1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜑)

Proof of Theorem simp2r1
StepHypRef Expression
1 simpr1 1195 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜑)
213ad2ant2 1135 1 ((𝜏 ∧ (𝜃 ∧ (𝜑𝜓𝜒)) ∧ 𝜂) → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 399  w3a 1088
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 210  df-an 400  df-3an 1090
This theorem is referenced by:  btwnconn1lem8  34052  btwnconn1lem9  34053  btwnconn1lem10  34054  btwnconn1lem11  34055  btwnconn1lem12  34056  jm2.27  40443
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