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Mirrors > Home > MPE Home > Th. List > Mathboxes > equcomi1 | Structured version Visualization version GIF version |
Description: Proof of equcomi 2021 from equid1 37411, avoiding use of ax-5 1914 (the only use of ax-5 1914 is via ax7 2020, so using ax-7 2012 instead would remove dependency on ax-5 1914). (Contributed by BJ, 8-Jul-2021.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
equcomi1 | ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid1 37411 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | ax7 2020 | . 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑥 → 𝑦 = 𝑥)) | |
3 | 1, 2 | mpi 20 | 1 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
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-c5 37395 ax-c4 37396 ax-c7 37397 ax-c10 37398 ax-c9 37402 |
This theorem depends on definitions: df-bi 206 df-an 398 df-ex 1783 |
This theorem is referenced by: aecom-o 37413 |
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