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Mirrors > Home > ILE Home > Th. List > ralim | Unicode version |
Description: Distribution of restricted quantification over implication. (Contributed by NM, 9-Feb-1997.) |
Ref | Expression |
---|---|
ralim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2449 | . . 3 | |
2 | ax-2 7 | . . . 4 | |
3 | 2 | al2imi 1446 | . . 3 |
4 | 1, 3 | sylbi 120 | . 2 |
5 | df-ral 2449 | . 2 | |
6 | df-ral 2449 | . 2 | |
7 | 4, 5, 6 | 3imtr4g 204 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1341 wcel 2136 wral 2444 |
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 1435 ax-gen 1437 |
This theorem depends on definitions: df-bi 116 df-ral 2449 |
This theorem is referenced by: ral2imi 2531 trint 4095 peano2 4572 mpteqb 5576 mptelixpg 6700 lbzbi 9554 r19.29uz 10934 alzdvds 11792 |
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