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Mirrors > Home > MPE Home > Th. List > Mathboxes > equncomiVD | Structured version Visualization version GIF version |
Description: Inference form of equncom 3720. 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 3721 is equncomiVD 38127 without
virtual deductions and was automatically derived from equncomiVD 38127.
|
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 3720 | . . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
3 | 2 | biimpi 205 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵)) |
4 | 1, 3 | e0a 38020 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∪ cun 3538 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-un 3545 |
This theorem is referenced by: (None) |
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