![]() |
Mathbox for BJ |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > axc11n11 | Structured version Visualization version GIF version |
Description: Proof of axc11n 2295 from { ax-1 6-- ax-7 1922, axc11 2302 } . Almost identical to axc11nfromc11 33229. (Contributed by NM, 6-Jul-2021.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
axc11n11 | ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11 2302 | . . 3 ⊢ (∀𝑥 𝑥 = 𝑦 → (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑥 = 𝑦)) | |
2 | 1 | pm2.43i 50 | . 2 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑥 = 𝑦) |
3 | equcomi 1931 | . 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥) | |
4 | 2, 3 | sylg 1740 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1473 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-12 2034 ax-13 2234 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |