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 | uunTT1p1.1 | ⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) → 𝜓 ) | |
Assertion | uunTT1p1 | ⊢ ( 𝜑 → 𝜓 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uunTT1p1.1 | ⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) → 𝜓 ) | |
2 | 3ancomb | ⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ ⊤ ∧ 𝜑 ) ) | |
3 | 3anass | ⊢ ( ( ⊤ ∧ ⊤ ∧ 𝜑 ) ↔ ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) ) | |
4 | anabs5 | ⊢ ( ( ⊤ ∧ ( ⊤ ∧ 𝜑 ) ) ↔ ( ⊤ ∧ 𝜑 ) ) | |
5 | 2 3 4 | 3bitri | ⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ ( ⊤ ∧ 𝜑 ) ) |
6 | truan | ⊢ ( ( ⊤ ∧ 𝜑 ) ↔ 𝜑 ) | |
7 | 5 6 | bitri | ⊢ ( ( ⊤ ∧ 𝜑 ∧ ⊤ ) ↔ 𝜑 ) |
8 | 7 1 | sylbir | ⊢ ( 𝜑 → 𝜓 ) |