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Theorem mp3an2ani 1429
Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
mp3an2ani.1 𝜑
mp3an2ani.2 (𝜓𝜒)
mp3an2ani.3 ((𝜓𝜃) → 𝜏)
mp3an2ani.4 ((𝜑𝜒𝜏) → 𝜂)
Assertion
Ref Expression
mp3an2ani ((𝜓𝜃) → 𝜂)

Proof of Theorem mp3an2ani
StepHypRef Expression
1 mp3an2ani.1 . . 3 𝜑
2 mp3an2ani.2 . . 3 (𝜓𝜒)
3 mp3an2ani.3 . . 3 ((𝜓𝜃) → 𝜏)
4 mp3an2ani.4 . . 3 ((𝜑𝜒𝜏) → 𝜂)
51, 2, 3, 4mp3an3an 1428 . 2 ((𝜓 ∧ (𝜓𝜃)) → 𝜂)
65anabss5 856 1 ((𝜓𝜃) → 𝜂)
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:  2lgsoddprmlem2  25115  isosctrlem1ALT  38990  odz2prm2pw  41240  lighneallem4  41292
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