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Mirrors > Home > ILE Home > Th. List > csbfv12g | Unicode version |
Description: Move class substitution in and out of a function value. (Contributed by NM, 11-Nov-2005.) |
Ref | Expression |
---|---|
csbfv12g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbiotag 5111 | . . 3 | |
2 | sbcbrg 3977 | . . . . 5 | |
3 | csbconstg 3011 | . . . . . 6 | |
4 | 3 | breq2d 3936 | . . . . 5 |
5 | 2, 4 | bitrd 187 | . . . 4 |
6 | 5 | iotabidv 5104 | . . 3 |
7 | 1, 6 | eqtrd 2170 | . 2 |
8 | df-fv 5126 | . . 3 | |
9 | 8 | csbeq2i 3024 | . 2 |
10 | df-fv 5126 | . 2 | |
11 | 7, 9, 10 | 3eqtr4g 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wcel 1480 wsbc 2904 csb 2998 class class class wbr 3924 cio 5081 cfv 5118 |
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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-sbc 2905 df-csb 2999 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-br 3925 df-iota 5083 df-fv 5126 |
This theorem is referenced by: csbfv2g 5451 |
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