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Mirrors > Home > MPE Home > Th. List > Mathboxes > equncomiVD | Structured version Visualization version GIF version |
Description: Inference form of equncom 4153. 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 4154 is equncomiVD 43563 without
virtual deductions and was automatically derived from equncomiVD 43563.
|
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 4153 | . . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
3 | 2 | biimpi 215 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵)) |
4 | 1, 3 | e0a 43466 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∪ cun 3945 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3477 df-un 3952 |
This theorem is referenced by: (None) |
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