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Mirrors > Home > MPE Home > Th. List > Mathboxes > equncomiVD | Structured version Visualization version GIF version |
Description: Inference form of equncom 3758. 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 3759 is equncomiVD 39105 without
virtual deductions and was automatically derived from equncomiVD 39105.
|
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 3758 | . . 3 ⊢ (𝐴 = (𝐵 ∪ 𝐶) ↔ 𝐴 = (𝐶 ∪ 𝐵)) | |
3 | 2 | biimpi 206 | . 2 ⊢ (𝐴 = (𝐵 ∪ 𝐶) → 𝐴 = (𝐶 ∪ 𝐵)) |
4 | 1, 3 | e0a 38999 | 1 ⊢ 𝐴 = (𝐶 ∪ 𝐵) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1483 ∪ cun 3572 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 |
This theorem is referenced by: (None) |
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