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Theorem ee200 41278
Description: e200 41277 without virtual deductions. (Contributed by Alan Sare, 13-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee200.1 (𝜑 → (𝜓𝜒))
ee200.2 𝜃
ee200.3 𝜏
ee200.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee200 (𝜑 → (𝜓𝜂))

Proof of Theorem ee200
StepHypRef Expression
1 ee200.1 . 2 (𝜑 → (𝜓𝜒))
2 ee200.2 . . . 4 𝜃
32a1i 11 . . 3 (𝜓𝜃)
43a1i 11 . 2 (𝜑 → (𝜓𝜃))
5 ee200.3 . . . 4 𝜏
65a1i 11 . . 3 (𝜓𝜏)
76a1i 11 . 2 (𝜑 → (𝜓𝜏))
8 ee200.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
91, 4, 7, 8ee222 41132 1 (𝜑 → (𝜓𝜂))
Colors of variables: wff setvar class
Syntax hints:  wi 4
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 210  df-an 400
This theorem is referenced by: (None)
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