Description: A deduction unionizing a non-unionized collection of virtual hypotheses. (Contributed by Alan Sare, 3-Dec-2015) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | un2122.1 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ∧ 𝜓 ) → 𝜒 ) | |
| Assertion | un2122 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | un2122.1 | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ∧ 𝜓 ) → 𝜒 ) | |
| 2 | 3anass | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜓 ∧ 𝜓 ) ) ) | |
| 3 | anandir | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜓 ∧ 𝜓 ) ) ) | |
| 4 | ancom | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) ) | |
| 5 | anabs7 | ⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) ) | |
| 6 | 4 5 | bitri | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ) ) |
| 7 | 3 6 | bitr3i | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜓 ∧ 𝜓 ) ) ↔ ( 𝜑 ∧ 𝜓 ) ) |
| 8 | 2 7 | bitri | ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜓 ∧ 𝜓 ) ↔ ( 𝜑 ∧ 𝜓 ) ) |
| 9 | 8 1 | sylbir | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |