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Mirrors > Home > ILE Home > Th. List > ralbi | Unicode version |
Description: Distribute a restricted universal quantifier over a biconditional. Theorem 19.15 of [Margaris] p. 90 with restricted quantification. (Contributed by NM, 6-Oct-2003.) |
Ref | Expression |
---|---|
ralbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2466 | . 2 | |
2 | rsp 2480 | . . 3 | |
3 | 2 | imp 123 | . 2 |
4 | 1, 3 | ralbida 2431 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 1480 wral 2416 |
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 1423 ax-gen 1425 ax-4 1487 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-ral 2421 |
This theorem is referenced by: uniiunlem 3185 iineq2 3830 ralrnmpt 5562 f1mpt 5672 mpo2eqb 5880 ralrnmpo 5885 cau3lem 10886 |
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