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Theorem jad 174
Description: Deduction form of ja 173. (Contributed by Scott Fenton, 13-Dec-2010.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Hypotheses
Ref Expression
jad.1 (𝜑 → (¬ 𝜓𝜃))
jad.2 (𝜑 → (𝜒𝜃))
Assertion
Ref Expression
jad (𝜑 → ((𝜓𝜒) → 𝜃))

Proof of Theorem jad
StepHypRef Expression
1 jad.1 . . . 4 (𝜑 → (¬ 𝜓𝜃))
21com12 32 . . 3 𝜓 → (𝜑𝜃))
3 jad.2 . . . 4 (𝜑 → (𝜒𝜃))
43com12 32 . . 3 (𝜒 → (𝜑𝜃))
52, 4ja 173 . 2 ((𝜓𝜒) → (𝜑𝜃))
65com12 32 1 (𝜑 → ((𝜓𝜒) → 𝜃))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm2.6  182  pm2.65  184  merco2  1659  nfimdOLDOLD  1822  wereu2  5101  isfin7-2  9203  axpowndlem3  9406  suppssfz  12777  lo1bdd2  14236  pntlem3  25279  hbimtg  31686  arg-ax  32390  onsuct0  32415  ordcmp  32421  poimirlem26  33406  ax12indi  34048  ntrneiiso  38209  hbimpg  38590
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