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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 399  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 210  df-an 400  df-3an 1086
This theorem is referenced by:  nllyrest  22100  cdlemblem  37061  cdleme21  37605  cdleme22b  37609  cdleme40m  37735  cdlemg34  37980  cdlemk5u  38129  cdlemk6u  38130  cdlemk21N  38141  cdlemk20  38142  cdlemk26b-3  38173  cdlemk26-3  38174  cdlemk28-3  38176  cdlemky  38194  cdlemk11t  38214  cdlemkyyN  38230  stoweidlem56  42651
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