Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > axc4i | GIF version |
Description: Inference version of 19.21 1563. (Contributed by NM, 3-Jan-1993.) |
Ref | Expression |
---|---|
axc4i.1 | ⊢ (∀𝑥𝜑 → 𝜓) |
Ref | Expression |
---|---|
axc4i | ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1521 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | axc4i.1 | . 2 ⊢ (∀𝑥𝜑 → 𝜓) | |
3 | 1, 2 | alrimi 1502 | 1 ⊢ (∀𝑥𝜑 → ∀𝑥𝜓) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∀wal 1333 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1427 ax-gen 1429 ax-4 1490 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1441 |
This theorem is referenced by: nfabdw 2318 |
Copyright terms: Public domain | W3C validator |