![]() |
Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > equcomi1 | Structured version Visualization version GIF version |
Description: Proof of equcomi 2020 from equid1 37764, avoiding use of ax-5 1913 (the only use of ax-5 1913 is via ax7 2019, so using ax-7 2011 instead would remove dependency on ax-5 1913). (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 37764 | . 2 ⊢ 𝑥 = 𝑥 | |
2 | ax7 2019 | . 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 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-c5 37748 ax-c4 37749 ax-c7 37750 ax-c10 37751 ax-c9 37755 |
This theorem depends on definitions: df-bi 206 df-an 397 df-ex 1782 |
This theorem is referenced by: aecom-o 37766 |
Copyright terms: Public domain | W3C validator |