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Mirrors > Home > MPE Home > Th. List > r19.12sn | Structured version Visualization version Unicode version |
Description: Special case of r19.12 3063 where its converse holds. (Contributed by NM, 19-May-2008.) (Revised by Mario Carneiro, 23-Apr-2015.) (Revised by BJ, 18-Mar-2020.) |
Ref | Expression |
---|---|
r19.12sn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcralg 3513 | . 2 | |
2 | rexsns 4217 | . 2 | |
3 | rexsns 4217 | . . 3 | |
4 | 3 | ralbii 2980 | . 2 |
5 | 1, 2, 4 | 3bitr4g 303 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wcel 1990 wral 2912 wrex 2913 wsbc 3435 csn 4177 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-v 3202 df-sbc 3436 df-sn 4178 |
This theorem is referenced by: intimasn 37949 |
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