Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > csbopabgALT | Structured version Visualization version Unicode version |
Description: Move substitution into a class abstraction. Version of csbopab 5008 with a sethood antecedent but depending on fewer axioms. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) (New usage is discouraged.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
csbopabgALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3536 | . . 3 | |
2 | dfsbcq2 3438 | . . . 4 | |
3 | 2 | opabbidv 4716 | . . 3 |
4 | 1, 3 | eqeq12d 2637 | . 2 |
5 | vex 3203 | . . 3 | |
6 | nfs1v 2437 | . . . 4 | |
7 | 6 | nfopab 4718 | . . 3 |
8 | sbequ12 2111 | . . . 4 | |
9 | 8 | opabbidv 4716 | . . 3 |
10 | 5, 7, 9 | csbief 3558 | . 2 |
11 | 4, 10 | vtoclg 3266 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 wsb 1880 wcel 1990 wsbc 3435 csb 3533 copab 4712 |
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-v 3202 df-sbc 3436 df-csb 3534 df-opab 4713 |
This theorem is referenced by: csbcnvgALT 5307 |
Copyright terms: Public domain | W3C validator |