Metamath Proof Explorer


Theorem uunT12p5

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.)

Ref Expression
Hypothesis uunT12p5.1 ( ( 𝜓𝜑 ∧ ⊤ ) → 𝜒 )
Assertion uunT12p5 ( ( 𝜑𝜓 ) → 𝜒 )

Proof

Step Hyp Ref Expression
1 uunT12p5.1 ( ( 𝜓𝜑 ∧ ⊤ ) → 𝜒 )
2 3anrev ( ( 𝜓𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ 𝜑𝜓 ) )
3 3anass ( ( ⊤ ∧ 𝜑𝜓 ) ↔ ( ⊤ ∧ ( 𝜑𝜓 ) ) )
4 2 3 bitri ( ( 𝜓𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ ( 𝜑𝜓 ) ) )
5 truan ( ( ⊤ ∧ ( 𝜑𝜓 ) ) ↔ ( 𝜑𝜓 ) )
6 4 5 bitri ( ( 𝜓𝜑 ∧ ⊤ ) ↔ ( 𝜑𝜓 ) )
7 6 1 sylbir ( ( 𝜑𝜓 ) → 𝜒 )