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Theorem uunT12p4 40999
Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
uunT12p4.1 ((𝜑𝜓 ∧ ⊤) → 𝜒)
Assertion
Ref Expression
uunT12p4 ((𝜑𝜓) → 𝜒)

Proof of Theorem uunT12p4
StepHypRef Expression
1 3anrot 1094 . . . 4 ((⊤ ∧ 𝜑𝜓) ↔ (𝜑𝜓 ∧ ⊤))
2 3anass 1089 . . . 4 ((⊤ ∧ 𝜑𝜓) ↔ (⊤ ∧ (𝜑𝜓)))
31, 2bitr3i 278 . . 3 ((𝜑𝜓 ∧ ⊤) ↔ (⊤ ∧ (𝜑𝜓)))
4 truan 1541 . . 3 ((⊤ ∧ (𝜑𝜓)) ↔ (𝜑𝜓))
53, 4bitri 276 . 2 ((𝜑𝜓 ∧ ⊤) ↔ (𝜑𝜓))
6 uunT12p4.1 . 2 ((𝜑𝜓 ∧ ⊤) → 𝜒)
75, 6sylbir 236 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396  w3a 1081  wtru 1531
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 208  df-an 397  df-3an 1083  df-tru 1533
This theorem is referenced by: (None)
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