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Theorem eel1111 37968
 Description: Four-hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl112anc 1322 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.)
Hypotheses
Ref Expression
eel1111.1 (𝜑𝜓)
eel1111.2 (𝜑𝜒)
eel1111.3 (𝜑𝜃)
eel1111.4 (𝜑𝜏)
eel1111.5 ((((𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)
Assertion
Ref Expression
eel1111 (𝜑𝜂)

Proof of Theorem eel1111
StepHypRef Expression
1 eel1111.4 . 2 (𝜑𝜏)
2 eel1111.1 . . 3 (𝜑𝜓)
3 eel1111.2 . . 3 (𝜑𝜒)
4 eel1111.3 . . 3 (𝜑𝜃)
5 eel1111.5 . . . 4 ((((𝜓𝜒) ∧ 𝜃) ∧ 𝜏) → 𝜂)
65exp41 636 . . 3 (𝜓 → (𝜒 → (𝜃 → (𝜏𝜂))))
72, 3, 4, 6syl3c 64 . 2 (𝜑 → (𝜏𝜂))
81, 7mpd 15 1 (𝜑𝜂)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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 This theorem is referenced by:  sineq0ALT  38195
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