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Mirrors > Home > MPE Home > Th. List > rspc2vd | Structured version Visualization version Unicode version |
Description: Deduction version of 2-variable restricted specialization, using implicit substitution. Notice that the class for the second set variable may depend on the first set variable . (Contributed by AV, 29-Mar-2021.) |
Ref | Expression |
---|---|
rspc2vd.a | |
rspc2vd.b | |
rspc2vd.c | |
rspc2vd.d | |
rspc2vd.e |
Ref | Expression |
---|---|
rspc2vd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rspc2vd.e | . . 3 | |
2 | rspc2vd.c | . . . 4 | |
3 | rspc2vd.d | . . . 4 | |
4 | 2, 3 | csbied 3560 | . . 3 |
5 | 1, 4 | eleqtrrd 2704 | . 2 |
6 | nfcsb1v 3549 | . . . . 5 | |
7 | nfv 1843 | . . . . 5 | |
8 | 6, 7 | nfral 2945 | . . . 4 |
9 | csbeq1a 3542 | . . . . 5 | |
10 | rspc2vd.a | . . . . 5 | |
11 | 9, 10 | raleqbidv 3152 | . . . 4 |
12 | 8, 11 | rspc 3303 | . . 3 |
13 | 2, 12 | syl 17 | . 2 |
14 | rspc2vd.b | . . 3 | |
15 | 14 | rspcv 3305 | . 2 |
16 | 5, 13, 15 | sylsyld 61 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 csb 3533 |
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-v 3202 df-sbc 3436 df-csb 3534 |
This theorem is referenced by: frcond1 27130 frgrwopreglem4a 27174 |
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