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Theorem uun0.1 38026
 Description: Convention notation form of un0.1 38027. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
uun0.1.1 (⊤ → 𝜑)
uun0.1.2 (𝜓𝜒)
uun0.1.3 ((⊤ ∧ 𝜓) → 𝜃)
Assertion
Ref Expression
uun0.1 (𝜓𝜃)

Proof of Theorem uun0.1
StepHypRef Expression
1 tru 1479 . 2
2 uun0.1.1 . . . . . 6 (⊤ → 𝜑)
3 uun0.1.2 . . . . . 6 (𝜓𝜒)
42, 3pm3.2i 470 . . . . 5 ((⊤ → 𝜑) ∧ (𝜓𝜒))
5 uun0.1.3 . . . . 5 ((⊤ ∧ 𝜓) → 𝜃)
64, 5pm3.2i 470 . . . 4 (((⊤ → 𝜑) ∧ (𝜓𝜒)) ∧ ((⊤ ∧ 𝜓) → 𝜃))
76simpri 477 . . 3 ((⊤ ∧ 𝜓) → 𝜃)
87ex 449 . 2 (⊤ → (𝜓𝜃))
91, 8ax-mp 5 1 (𝜓𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383  ⊤wtru 1476 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-tru 1478 This theorem is referenced by:  un0.1  38027  sspwimp  38176
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