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Theorem jad 188
Description: Deduction form of ja 187. (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 187 . 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  192  pm2.65  194  merco2  1730  wereu2  5551  isfin7-2  9807  axpowndlem3  10010  suppssfz  13352  lo1bdd2  14871  pntlem3  26099  hbimtg  32935  frpomin  32962  arg-ax  33648  onsuct0  33673  ordcmp  33679  poimirlem26  34785  ax12indi  35947  ntrneiiso  40306  hbimpg  40753
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