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Theorem uunT12p1 39546
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
uunT12p1.1 ((⊤ ∧ 𝜓𝜑) → 𝜒)
Assertion
Ref Expression
uunT12p1 ((𝜑𝜓) → 𝜒)

Proof of Theorem uunT12p1
StepHypRef Expression
1 3anass 1079 . . . 4 ((⊤ ∧ 𝜓𝜑) ↔ (⊤ ∧ (𝜓𝜑)))
2 truan 1648 . . . 4 ((⊤ ∧ (𝜓𝜑)) ↔ (𝜓𝜑))
31, 2bitri 264 . . 3 ((⊤ ∧ 𝜓𝜑) ↔ (𝜓𝜑))
4 ancom 452 . . 3 ((𝜑𝜓) ↔ (𝜓𝜑))
53, 4bitr4i 267 . 2 ((⊤ ∧ 𝜓𝜑) ↔ (𝜑𝜓))
6 uunT12p1.1 . 2 ((⊤ ∧ 𝜓𝜑) → 𝜒)
75, 6sylbir 225 1 ((𝜑𝜓) → 𝜒)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1070  wtru 1631
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-an 383  df-3an 1072  df-tru 1633
This theorem is referenced by: (None)
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