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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2395 |
. . 3
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2 | ax-2 6 |
. . . 4
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3 | 2 | al2imi 1417 |
. . 3
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4 | 1, 3 | sylbi 120 |
. 2
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5 | df-ral 2395 |
. 2
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6 | df-ral 2395 |
. 2
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7 | 4, 5, 6 | 3imtr4g 204 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1406 ax-gen 1408 |
This theorem depends on definitions: df-bi 116 df-ral 2395 |
This theorem is referenced by: ral2imi 2471 trint 4001 peano2 4469 mpteqb 5465 mptelixpg 6582 lbzbi 9310 r19.29uz 10656 alzdvds 11400 |
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