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Theorem simpr3r 1121
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simpr3r ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)

Proof of Theorem simpr3r
StepHypRef Expression
1 simp3r 1088 . 2 ((𝜒𝜃 ∧ (𝜑𝜓)) → 𝜓)
21adantl 482 1 ((𝜏 ∧ (𝜒𝜃 ∧ (𝜑𝜓))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1036
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 386  df-3an 1038
This theorem is referenced by:  ax5seg  25718  segconeq  31759  ifscgr  31793  btwnconn1lem9  31844  btwnconn1lem11  31846  btwnconn1lem12  31847  lplnexllnN  34330  cdleme3b  34996  cdleme3c  34997  cdleme3e  34999  cdleme27a  35135
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