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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 2444 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 2444 | 1 ⊢ (∀𝑥 𝑥 = 𝑦 → ∀𝑦 𝑦 = 𝑥) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∀wal 1531 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-10 2141 ax-12 2173 ax-13 2386 |
This theorem depends on definitions: df-bi 209 df-an 399 df-ex 1777 df-nf 1781 |
This theorem is referenced by: (None) |
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