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Mirrors > Home > ILE Home > Th. List > rexbi | Unicode version |
Description: Distribute a restricted existential quantifier over a biconditional. Theorem 19.18 of [Margaris] p. 90 with restricted quantification. (Contributed by Jim Kingdon, 21-Jan-2019.) |
Ref | Expression |
---|---|
rexbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfra1 2501 | . 2 | |
2 | rsp 2517 | . . 3 | |
3 | 2 | imp 123 | . 2 |
4 | 1, 3 | rexbida 2465 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 2141 wral 2448 wrex 2449 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-ial 1527 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-ral 2453 df-rex 2454 |
This theorem is referenced by: rexrnmpo 5968 |
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