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Theorem eel2122old 37964
 Description: el2122old 37965 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
eel2122old.1 ((𝜑𝜓) → 𝜒)
eel2122old.2 (𝜓𝜃)
eel2122old.3 (𝜓𝜏)
eel2122old.4 ((𝜒𝜃𝜏) → 𝜂)
Assertion
Ref Expression
eel2122old ((𝜑𝜓) → 𝜂)

Proof of Theorem eel2122old
StepHypRef Expression
1 eel2122old.3 . . . . . 6 (𝜓𝜏)
2 eel2122old.2 . . . . . . 7 (𝜓𝜃)
3 eel2122old.1 . . . . . . . 8 ((𝜑𝜓) → 𝜒)
4 eel2122old.4 . . . . . . . . 9 ((𝜒𝜃𝜏) → 𝜂)
543exp 1256 . . . . . . . 8 (𝜒 → (𝜃 → (𝜏𝜂)))
63, 5syl 17 . . . . . . 7 ((𝜑𝜓) → (𝜃 → (𝜏𝜂)))
72, 6syl5 33 . . . . . 6 ((𝜑𝜓) → (𝜓 → (𝜏𝜂)))
81, 7syl7 72 . . . . 5 ((𝜑𝜓) → (𝜓 → (𝜓𝜂)))
98ex 449 . . . 4 (𝜑 → (𝜓 → (𝜓 → (𝜓𝜂))))
109pm2.43d 51 . . 3 (𝜑 → (𝜓 → (𝜓𝜂)))
1110pm2.43d 51 . 2 (𝜑 → (𝜓𝜂))
1211imp 444 1 ((𝜑𝜓) → 𝜂)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383   ∧ w3a 1031 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 196  df-an 385  df-3an 1033 This theorem is referenced by:  el2122old  37965  suctrALTcf  38180
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