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Theorem ee222 44500
Description: e222 44634 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 7-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee222.1 (𝜑 → (𝜓𝜒))
ee222.2 (𝜑 → (𝜓𝜃))
ee222.3 (𝜑 → (𝜓𝜏))
ee222.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee222 (𝜑 → (𝜓𝜂))

Proof of Theorem ee222
StepHypRef Expression
1 ee222.1 . . . 4 (𝜑 → (𝜓𝜒))
21imp 406 . . 3 ((𝜑𝜓) → 𝜒)
3 ee222.2 . . . 4 (𝜑 → (𝜓𝜃))
43imp 406 . . 3 ((𝜑𝜓) → 𝜃)
5 ee222.3 . . . 4 (𝜑 → (𝜓𝜏))
65imp 406 . . 3 ((𝜑𝜓) → 𝜏)
7 ee222.4 . . 3 (𝜒 → (𝜃 → (𝜏𝜂)))
82, 4, 6, 7syl3c 66 . 2 ((𝜑𝜓) → 𝜂)
98ex 412 1 (𝜑 → (𝜓𝜂))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395
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 207  df-an 396
This theorem is referenced by:  ee121  44503  ee122  44504  tratrb  44534  ee220  44636  ee202  44638  ee022  44640  ee002  44642  ee020  44644  ee200  44646  ee221  44648  ee212  44650  ee112  44653  ee211  44656  ee210  44658  ee201  44660  ee120  44662  ee021  44664  ee012  44666  ee102  44668  suctrALT2  44835
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