![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > axi10 | Structured version Visualization version GIF version |
Description: Axiom of Quantifier Substitution (intuitionistic logic axiom ax-10). This is just axc11n 2295 by another name. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.) |
Ref | Expression |
---|---|
axi10 | ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | axc11n 2295 | 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 |