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 | uunT12p3.1 | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) → 𝜒 ) | |
| Assertion | uunT12p3 | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | uunT12p3.1 | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) → 𝜒 ) | |
| 2 | 3ancoma | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) ↔ ( ⊤ ∧ 𝜓 ∧ 𝜑 ) ) | |
| 3 | 3anass | ⊢ ( ( ⊤ ∧ 𝜓 ∧ 𝜑 ) ↔ ( ⊤ ∧ ( 𝜓 ∧ 𝜑 ) ) ) | |
| 4 | 2 3 | bitri | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) ↔ ( ⊤ ∧ ( 𝜓 ∧ 𝜑 ) ) ) |
| 5 | truan | ⊢ ( ( ⊤ ∧ ( 𝜓 ∧ 𝜑 ) ) ↔ ( 𝜓 ∧ 𝜑 ) ) | |
| 6 | 4 5 | bitri | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜑 ) ) |
| 7 | ancom | ⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ( 𝜓 ∧ 𝜑 ) ) | |
| 8 | 6 7 | bitr4i | ⊢ ( ( 𝜓 ∧ ⊤ ∧ 𝜑 ) ↔ ( 𝜑 ∧ 𝜓 ) ) |
| 9 | 8 1 | sylbir | ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 ) |