Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ralcom3 | Unicode version |
Description: A commutative law for restricted quantifiers that swaps the domain of the restriction. (Contributed by NM, 22-Feb-2004.) |
Ref | Expression |
---|---|
ralcom3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm2.04 82 | . . 3 | |
2 | 1 | ralimi2 2535 | . 2 |
3 | pm2.04 82 | . . 3 | |
4 | 3 | ralimi2 2535 | . 2 |
5 | 2, 4 | impbii 126 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 105 wcel 2146 wral 2453 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1445 ax-gen 1447 |
This theorem depends on definitions: df-bi 117 df-ral 2458 |
This theorem is referenced by: zfregfr 4567 tgss2 13072 |
Copyright terms: Public domain | W3C validator |