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Theorem ee220 39621
Description: e220 39620 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee220.1 (𝜑 → (𝜓𝜒))
ee220.2 (𝜑 → (𝜓𝜃))
ee220.3 𝜏
ee220.4 (𝜒 → (𝜃 → (𝜏𝜂)))
Assertion
Ref Expression
ee220 (𝜑 → (𝜓𝜂))

Proof of Theorem ee220
StepHypRef Expression
1 ee220.1 . 2 (𝜑 → (𝜓𝜒))
2 ee220.2 . 2 (𝜑 → (𝜓𝜃))
3 ee220.3 . . 3 𝜏
432a1i 12 . 2 (𝜑 → (𝜓𝜏))
5 ee220.4 . 2 (𝜒 → (𝜃 → (𝜏𝜂)))
61, 2, 4, 5ee222 39476 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 199  df-an 386
This theorem is referenced by: (None)
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