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Theorem mp3an12i 1420
 Description: mp3an 1416 with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016.)
Hypotheses
Ref Expression
mp3an12i.1 𝜑
mp3an12i.2 𝜓
mp3an12i.3 (𝜒𝜃)
mp3an12i.4 ((𝜑𝜓𝜃) → 𝜏)
Assertion
Ref Expression
mp3an12i (𝜒𝜏)

Proof of Theorem mp3an12i
StepHypRef Expression
1 mp3an12i.3 . 2 (𝜒𝜃)
2 mp3an12i.1 . . 3 𝜑
3 mp3an12i.2 . . 3 𝜓
4 mp3an12i.4 . . 3 ((𝜑𝜓𝜃) → 𝜏)
52, 3, 4mp3an12 1406 . 2 (𝜃𝜏)
61, 5syl 17 1 (𝜒𝜏)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  ener  7888  hashfun  13084  funcnvs2  13508  3dvds  14890  oddp1d2  14920  bitsres  15033  bposlem9  24817  gausslemma2dlem1  24891  poimirlem26  32605  mblfinlem2  32617  isosctrlem1ALT  38192  fmtnorec1  39987  evengpoap3  40215  umgr2v2e  40741  0wlkOnlem2  41287
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