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Theorem ee120 41290
Description: Virtual deduction rule e120 41289 without virtual deduction symbols. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee120.1 (𝜑𝜓)
ee120.2 (𝜑 → (𝜒𝜃))
ee120.3 𝜏
ee120.4 (𝜓 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee120 (𝜑 → (𝜒𝜂))

Proof of Theorem ee120
StepHypRef Expression
1 ee120.1 . . 3 (𝜑𝜓)
21a1d 25 . 2 (𝜑 → (𝜒𝜓))
3 ee120.2 . 2 (𝜑 → (𝜒𝜃))
4 ee120.3 . . . 4 𝜏
54a1i 11 . . 3 (𝜒𝜏)
65a1i 11 . 2 (𝜑 → (𝜒𝜏))
7 ee120.4 . 2 (𝜓 → (𝜃 → (𝜏𝜂)))
82, 3, 6, 7ee222 41128 1 (𝜑 → (𝜒𝜂))
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)
  Copyright terms: Public domain W3C validator