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Mirrors > Home > MPE Home > Th. List > Mathboxes > equncomiVD | Structured version Visualization version GIF version |
Description: Inference form of equncom 4130. 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 4131 is equncomiVD 41223 without
virtual deductions and was automatically derived from equncomiVD 41223.
|
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 4130 | . . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
3 | 2 | biimpi 218 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵)) |
4 | 1, 3 | e0a 41126 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ∪ cun 3934 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2116 ax-9 2124 ax-10 2145 ax-11 2161 ax-12 2177 ax-ext 2793 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-tru 1540 df-ex 1781 df-nf 1785 df-sb 2070 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-v 3496 df-un 3941 |
This theorem is referenced by: (None) |
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