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Mirrors > Home > MPE Home > Th. List > rexeqf | Structured version Visualization version Unicode version |
Description: Equality theorem for restricted existential quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 9-Oct-2003.) (Revised by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
raleq1f.1 |
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raleq1f.2 |
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Ref | Expression |
---|---|
rexeqf |
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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 2613 |
. . 3
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4 | eleq2 2528 |
. . . 4
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5 | 4 | anbi1d 716 |
. . 3
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6 | 3, 5 | exbid 1974 |
. 2
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7 | df-rex 2754 |
. 2
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8 | df-rex 2754 |
. 2
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9 | 6, 7, 8 | 3bitr4g 296 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-ext 2441 |
This theorem depends on definitions: df-bi 190 df-an 377 df-tru 1457 df-ex 1674 df-nf 1678 df-cleq 2454 df-clel 2457 df-nfc 2591 df-rex 2754 |
This theorem is referenced by: rexeq 2999 rexeqbid 3011 zfrep6 6787 iuneq12daf 28218 indexa 32104 |
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