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 | uunT12p4.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ⊤ ) → 𝜒 ) | |
| Assertion | uunT12p4 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uunT12p4.1 | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ⊤ ) → 𝜒 ) | |
| 2 | 3anrot | ⊢ ( ( ⊤ ∧ 𝜑 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ∧ ⊤ ) ) | |
| 3 | 3anass | ⊢ ( ( ⊤ ∧ 𝜑 ∧ 𝜓 ) ↔ ( ⊤ ∧ ( 𝜑 ∧ 𝜓 ) ) ) | |
| 4 | 2 3 | bitr3i | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ⊤ ) ↔ ( ⊤ ∧ ( 𝜑 ∧ 𝜓 ) ) ) |
| 5 | truan | ⊢ ( ( ⊤ ∧ ( 𝜑 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) ) | |
| 6 | 4 5 | bitri | ⊢ ( ( 𝜑 ∧ 𝜓 ∧ ⊤ ) ↔ ( 𝜑 ∧ 𝜓 ) ) |
| 7 | 6 1 | sylbir | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |