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Theorem uunT1p1 39533
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
uunT1p1.1 ((𝜑 ∧ ⊤) → 𝜓)
Assertion
Ref Expression
uunT1p1 (𝜑𝜓)

Proof of Theorem uunT1p1
StepHypRef Expression
1 ancom 452 . . 3 ((𝜑 ∧ ⊤) ↔ (⊤ ∧ 𝜑))
2 truan 1649 . . 3 ((⊤ ∧ 𝜑) ↔ 𝜑)
31, 2bitri 264 . 2 ((𝜑 ∧ ⊤) ↔ 𝜑)
4 uunT1p1.1 . 2 ((𝜑 ∧ ⊤) → 𝜓)
53, 4sylbir 225 1 (𝜑𝜓)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  wtru 1632
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-tru 1634
This theorem is referenced by: (None)
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