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Theorem simp3r2 1279
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.)
Assertion
Ref Expression
simp3r2 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)

Proof of Theorem simp3r2
StepHypRef Expression
1 simpr2 1192 . 2 ((𝜃 ∧ (𝜑𝜓𝜒)) → 𝜓)
213ad2ant3 1132 1 ((𝜏𝜂 ∧ (𝜃 ∧ (𝜑𝜓𝜒))) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 394  w3a 1084
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 206  df-an 395  df-3an 1086
This theorem is referenced by:  nllyrest  23408  cdlemblem  39270  cdleme21  39814  cdleme22b  39818  cdleme40m  39944  cdlemg34  40189  cdlemk5u  40338  cdlemk6u  40339  cdlemk21N  40350  cdlemk20  40351  cdlemk26b-3  40382  cdlemk26-3  40383  cdlemk28-3  40385  cdlemky  40403  cdlemk11t  40423  cdlemkyyN  40439  stoweidlem56  45446
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