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Mirrors > Home > ILE Home > Th. List > r19.2m | Unicode version |
Description: Theorem 19.2 of [Margaris] p. 89 with restricted quantifiers (compare 19.2 1649). The restricted version is valid only when the domain of quantification is inhabited. (Contributed by Jim Kingdon, 5-Aug-2018.) (Revised by Jim Kingdon, 7-Apr-2023.) |
Ref | Expression |
---|---|
r19.2m |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1w 2250 |
. . . 4
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2 | 1 | cbvexv 1930 |
. . 3
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3 | eleq1w 2250 |
. . . 4
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4 | 3 | cbvexv 1930 |
. . 3
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5 | 2, 4 | bitri 184 |
. 2
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6 | df-ral 2473 |
. . . . 5
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7 | exintr 1645 |
. . . . 5
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8 | 6, 7 | sylbi 121 |
. . . 4
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9 | df-rex 2474 |
. . . 4
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10 | 8, 9 | imbitrrdi 162 |
. . 3
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11 | 10 | impcom 125 |
. 2
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12 | 5, 11 | sylanbr 285 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-clel 2185 df-ral 2473 df-rex 2474 |
This theorem is referenced by: intssunim 3881 riinm 3974 iinexgm 4172 xpiindim 4782 cnviinm 5188 eusvobj2 5881 iinerm 6632 suplocexprlemml 7744 rexfiuz 11029 r19.2uz 11033 climuni 11332 pc2dvds 12361 issubg4m 13129 cncnp2m 14183 |
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