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Theorem ee03 38447
Description: e03 38446 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
ee03.1 𝜑
ee03.2 (𝜓 → (𝜒 → (𝜃𝜏)))
ee03.3 (𝜑 → (𝜏𝜂))
Assertion
Ref Expression
ee03 (𝜓 → (𝜒 → (𝜃𝜂)))

Proof of Theorem ee03
StepHypRef Expression
1 ee03.1 . . . . 5 𝜑
21a1i 11 . . . 4 (𝜓𝜑)
32a1d 25 . . 3 (𝜓 → (𝜒𝜑))
43a1dd 50 . 2 (𝜓 → (𝜒 → (𝜃𝜑)))
5 ee03.2 . 2 (𝜓 → (𝜒 → (𝜃𝜏)))
6 ee03.3 . 2 (𝜑 → (𝜏𝜂))
74, 5, 6ee33 38206 1 (𝜓 → (𝜒 → (𝜃𝜂)))
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
This theorem is referenced by:  ee03an  38449  suctrALT2  38552
  Copyright terms: Public domain W3C validator