Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ovig | Unicode version |
Description: The value of an operation class abstraction (weak version). (Unnecessary distinct variable restrictions were removed by David Abernethy, 19-Jun-2012.) (Contributed by NM, 14-Sep-1999.) (Revised by Mario Carneiro, 19-Dec-2013.) |
Ref | Expression |
---|---|
ovig.1 | |
ovig.2 | |
ovig.3 |
Ref | Expression |
---|---|
ovig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simpa 978 | . 2 | |
2 | eleq1 2200 | . . . . . 6 | |
3 | eleq1 2200 | . . . . . 6 | |
4 | 2, 3 | bi2anan9 595 | . . . . 5 |
5 | 4 | 3adant3 1001 | . . . 4 |
6 | ovig.1 | . . . 4 | |
7 | 5, 6 | anbi12d 464 | . . 3 |
8 | ovig.2 | . . . 4 | |
9 | moanimv 2072 | . . . 4 | |
10 | 8, 9 | mpbir 145 | . . 3 |
11 | ovig.3 | . . 3 | |
12 | 7, 10, 11 | ovigg 5884 | . 2 |
13 | 1, 12 | mpand 425 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wcel 1480 wmo 1998 (class class class)co 5767 coprab 5768 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-mo 2001 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-sbc 2905 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-opab 3985 df-id 4210 df-xp 4540 df-rel 4541 df-cnv 4542 df-co 4543 df-dm 4544 df-iota 5083 df-fun 5120 df-fv 5126 df-ov 5770 df-oprab 5771 |
This theorem is referenced by: th3q 6527 addnnnq0 7250 mulnnnq0 7251 addsrpr 7546 mulsrpr 7547 |
Copyright terms: Public domain | W3C validator |