Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > sbf2 | GIF version |
Description: Substitution has no effect on a bound variable. (Contributed by NM, 1-Jul-2005.) |
Ref | Expression |
---|---|
sbf2 | ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfa1 1506 | . 2 ⊢ Ⅎ𝑥∀𝑥𝜑 | |
2 | 1 | sbf 1735 | 1 ⊢ ([𝑦 / 𝑥]∀𝑥𝜑 ↔ ∀𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: ↔ wb 104 ∀wal 1314 [wsb 1720 |
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 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-4 1472 ax-i9 1495 ax-ial 1499 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |