Mathbox for Giovanni Mascellani |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > sbcexf | Structured version Visualization version Unicode version |
Description: Move existential quantifier in and out of class substitution, with an explicit non-free variable condition. (Contributed by Giovanni Mascellani, 29-May-2019.) |
Ref | Expression |
---|---|
sbcexf.1 |
Ref | Expression |
---|---|
sbcexf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1843 | . . . 4 | |
2 | 1 | sb8e 2425 | . . 3 |
3 | 2 | sbcbii 3491 | . 2 |
4 | sbcex2 3486 | . 2 | |
5 | sbcexf.1 | . . . 4 | |
6 | nfs1v 2437 | . . . 4 | |
7 | 5, 6 | nfsbc 3457 | . . 3 |
8 | nfv 1843 | . . 3 | |
9 | sbequ12r 2112 | . . . 4 | |
10 | 9 | sbcbidv 3490 | . . 3 |
11 | 7, 8, 10 | cbvex 2272 | . 2 |
12 | 3, 4, 11 | 3bitri 286 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wex 1704 wsb 1880 wnfc 2751 wsbc 3435 |
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-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 |
This theorem is referenced by: sbcexfi 33920 |
Copyright terms: Public domain | W3C validator |