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| Mirrors > Home > MPE Home > Th. List > Mathboxes > equncomiVD | Structured version Visualization version GIF version | ||
Description: Inference form of equncom 4159. The following User's Proof is a
Virtual Deduction proof completed automatically by the tools program
completeusersproof.cmd, which invokes Mel L. O'Cat's mmj2 and Norm
Megill's Metamath Proof Assistant. equncomi 4160 is equncomiVD 44889 without
virtual deductions and was automatically derived from equncomiVD 44889.
|
| Ref | Expression |
|---|---|
| equncomiVD.1 | ⊢ 𝐴 = (𝐵 ∪ 𝐶) |
| Ref | Expression |
|---|---|
| equncomiVD | ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equncomiVD.1 | . 2 ⊢ 𝐴 = (𝐵 ∪ 𝐶) | |
| 2 | equncom 4159 | . . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
| 3 | 2 | biimpi 216 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵)) |
| 4 | 1, 3 | e0a 44792 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 ∪ cun 3949 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3482 df-un 3956 |
| This theorem is referenced by: (None) |
| Copyright terms: Public domain | W3C validator |