Metamath Proof Explorer

Theorem uunT12p2

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 uunT12p2.1 ⊢ φ ∧ ⊤ ∧ ψ → χ
Assertion uunT12p2 ⊢ φ ∧ ψ → χ

Proof

Step Hyp Ref Expression
1 uunT12p2.1 ⊢ φ ∧ ⊤ ∧ ψ → χ
2 3anrot ⊢ φ ∧ ⊤ ∧ ψ ↔ ⊤ ∧ ψ ∧ φ
3 3anass ⊢ ⊤ ∧ ψ ∧ φ ↔ ⊤ ∧ ψ ∧ φ
4 2 3 bitri ⊢ φ ∧ ⊤ ∧ ψ ↔ ⊤ ∧ ψ ∧ φ
5 truan ⊢ ⊤ ∧ ψ ∧ φ ↔ ψ ∧ φ
6 4 5 bitri ⊢ φ ∧ ⊤ ∧ ψ ↔ ψ ∧ φ
7 ancom ⊢ φ ∧ ψ ↔ ψ ∧ φ
8 6 7 bitr4i ⊢ φ ∧ ⊤ ∧ ψ ↔ φ ∧ ψ
9 8 1 sylbir ⊢ φ ∧ ψ → χ