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Theorem uunT1 38528
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 3-Dec-2015.) Proof was revised to accomodate a possible future version of df-tru 1483. (Revised by David A. Wheeler, 8-May-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uunT1.1 ((⊤ ∧ 𝜑) → 𝜓)
Assertion
Ref Expression
uunT1 (𝜑𝜓)

Proof of Theorem uunT1
StepHypRef Expression
1 orc 400 . . 3 (𝜑 → (𝜑 ∨ ¬ 𝜑))
2 tru 1484 . . . . 5
3 biid 251 . . . . 5 (𝜑𝜑)
42, 32th 254 . . . 4 (⊤ ↔ (𝜑𝜑))
5 exmid 431 . . . . . 6 (𝜑 ∨ ¬ 𝜑)
65a1i 11 . . . . 5 ((𝜑𝜑) → (𝜑 ∨ ¬ 𝜑))
7 biidd 252 . . . . 5 ((𝜑 ∨ ¬ 𝜑) → (𝜑𝜑))
86, 7impbii 199 . . . 4 ((𝜑𝜑) ↔ (𝜑 ∨ ¬ 𝜑))
94, 8bitri 264 . . 3 (⊤ ↔ (𝜑 ∨ ¬ 𝜑))
101, 9sylibr 224 . 2 (𝜑 → ⊤)
11 uunT1.1 . 2 ((⊤ ∧ 𝜑) → 𝜓)
1210, 11mpancom 702 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wo 383  wa 384  wtru 1481
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 197  df-or 385  df-an 386  df-tru 1483
This theorem is referenced by:  uunT21  38530  sspwimpALT  38683
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