|   | Metamath Proof Explorer | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > axi4 | Structured version Visualization version GIF version | ||
| Description: Specialization (intuitionistic logic axiom ax-4). This is just sp 2182 by another name. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| axi4 | ⊢ (∀𝑥𝜑 → 𝜑) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | sp 2182 | 1 ⊢ (∀𝑥𝜑 → 𝜑) | 
| Colors of variables: wff setvar class | 
| Syntax hints: → wi 4 ∀wal 1537 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1794 ax-4 1808 ax-5 1909 ax-6 1966 ax-7 2006 ax-12 2176 | 
| This theorem depends on definitions: df-bi 207 df-ex 1779 | 
| This theorem is referenced by: (None) | 
| Copyright terms: Public domain | W3C validator |