![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > sbceq1d | Unicode version |
Description: Equality theorem for class substitution. (Contributed by Mario Carneiro, 9-Feb-2017.) (Revised by NM, 30-Jun-2018.) |
Ref | Expression |
---|---|
sbceq1d.1 |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
sbceq1d |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbceq1d.1 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | dfsbcq 2842 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | syl 14 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1381 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-4 1445 ax-17 1464 ax-ial 1472 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-cleq 2081 df-clel 2084 df-sbc 2841 |
This theorem is referenced by: sbceq1dd 2846 rexrnmpt 5442 findcard2 6605 findcard2s 6606 ac6sfi 6614 nn1suc 8441 uzind4s 9078 uzind4s2 9079 fzrevral 9519 fzshftral 9522 cjth 10280 prmind2 11380 bj-bdfindes 11844 bj-findes 11876 |
Copyright terms: Public domain | W3C validator |