Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ralrnmpt | Unicode version |
Description: A restricted quantifier over an image set. (Contributed by Mario Carneiro, 20-Aug-2015.) |
Ref | Expression |
---|---|
ralrnmpt.1 | |
ralrnmpt.2 |
Ref | Expression |
---|---|
ralrnmpt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralrnmpt.1 | . . . . 5 | |
2 | 1 | fnmpt 5299 | . . . 4 |
3 | dfsbcq 2939 | . . . . 5 | |
4 | 3 | ralrn 5608 | . . . 4 |
5 | 2, 4 | syl 14 | . . 3 |
6 | nfv 1508 | . . . . 5 | |
7 | nfsbc1v 2955 | . . . . 5 | |
8 | sbceq1a 2946 | . . . . 5 | |
9 | 6, 7, 8 | cbvral 2676 | . . . 4 |
10 | 9 | bicomi 131 | . . 3 |
11 | nfmpt1 4060 | . . . . . . 7 | |
12 | 1, 11 | nfcxfr 2296 | . . . . . 6 |
13 | nfcv 2299 | . . . . . 6 | |
14 | 12, 13 | nffv 5481 | . . . . 5 |
15 | nfv 1508 | . . . . 5 | |
16 | 14, 15 | nfsbc 2957 | . . . 4 |
17 | nfv 1508 | . . . 4 | |
18 | fveq2 5471 | . . . . 5 | |
19 | dfsbcq 2939 | . . . . 5 | |
20 | 18, 19 | syl 14 | . . . 4 |
21 | 16, 17, 20 | cbvral 2676 | . . 3 |
22 | 5, 10, 21 | 3bitr3g 221 | . 2 |
23 | 1 | fvmpt2 5554 | . . . . . 6 |
24 | dfsbcq 2939 | . . . . . 6 | |
25 | 23, 24 | syl 14 | . . . . 5 |
26 | ralrnmpt.2 | . . . . . . 7 | |
27 | 26 | sbcieg 2969 | . . . . . 6 |
28 | 27 | adantl 275 | . . . . 5 |
29 | 25, 28 | bitrd 187 | . . . 4 |
30 | 29 | ralimiaa 2519 | . . 3 |
31 | ralbi 2589 | . . 3 | |
32 | 30, 31 | syl 14 | . 2 |
33 | 22, 32 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 wral 2435 wsbc 2937 cmpt 4028 crn 4590 wfn 5168 cfv 5173 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4085 ax-pow 4138 ax-pr 4172 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-sbc 2938 df-csb 3032 df-un 3106 df-in 3108 df-ss 3115 df-pw 3546 df-sn 3567 df-pr 3568 df-op 3570 df-uni 3775 df-br 3968 df-opab 4029 df-mpt 4030 df-id 4256 df-xp 4595 df-rel 4596 df-cnv 4597 df-co 4598 df-dm 4599 df-rn 4600 df-iota 5138 df-fun 5175 df-fn 5176 df-fv 5181 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |