![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > sb8e | Structured version Visualization version Unicode version |
Description: Substitution of variable in existential quantifier. (Contributed by NM, 12-Aug-1993.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Jim Kingdon, 15-Jan-2018.) |
Ref | Expression |
---|---|
sb5rf.1 |
![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sb8e |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sb5rf.1 |
. 2
![]() ![]() ![]() ![]() | |
2 | 1 | nfs1 2196 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | sbequ12 2085 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | cbvex 2117 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1671 ax-4 1684 ax-5 1760 ax-6 1807 ax-7 1853 ax-10 1917 ax-11 1922 ax-12 1935 ax-13 2093 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1666 df-nf 1670 df-sb 1800 |
This theorem is referenced by: sbnf2 2270 2sb8e 2298 sb8mo 2335 mo3 2338 bnj985 29776 bj-mo3OLD 31459 sbcexf 32365 exlimddvfi 32374 pm11.58 36751 |
Copyright terms: Public domain | W3C validator |