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Mirrors > Home > ILE Home > Th. List > raleqf | Unicode version |
Description: Equality theorem for restricted universal quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 7-Mar-2004.) (Revised by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
raleq1f.1 |
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raleq1f.2 |
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Ref | Expression |
---|---|
raleqf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq1f.1 |
. . . 4
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2 | raleq1f.2 |
. . . 4
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3 | 1, 2 | nfeq 2327 |
. . 3
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4 | eleq2 2241 |
. . . 4
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5 | 4 | imbi1d 231 |
. . 3
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6 | 3, 5 | albid 1615 |
. 2
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7 | df-ral 2460 |
. 2
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8 | df-ral 2460 |
. 2
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9 | 6, 7, 8 | 3bitr4g 223 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 |
This theorem is referenced by: raleq 2672 repizf2 4159 ellimc3apf 13762 |
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