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Mirrors > Home > MPE Home > Th. List > ralsnsg | Structured version Unicode version |
Description: Substitution expressed in terms of quantification over a singleton. (Contributed by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralsnsg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc6g 3314 |
. 2
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2 | df-ral 2801 |
. . 3
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3 | elsn 3994 |
. . . . 5
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4 | 3 | imbi1i 325 |
. . . 4
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5 | 4 | albii 1611 |
. . 3
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6 | 2, 5 | bitri 249 |
. 2
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7 | 1, 6 | syl6rbbr 264 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-12 1794 ax-13 1954 ax-ext 2431 |
This theorem depends on definitions: df-bi 185 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2438 df-cleq 2444 df-clel 2447 df-ral 2801 df-v 3074 df-sbc 3289 df-sn 3981 |
This theorem is referenced by: ralsng 4015 sbcsngOLD 4036 ixpsnval 7371 ac6sfi 7662 rexfiuz 12948 prmind2 13887 finixpnum 28557 |
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