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Related theorems Unicode version |
| Description: A substitution into a
theorem remains true (when |
| Ref | Expression |
|---|---|
| sbcth.1 |
|
| Ref | Expression |
|---|---|
| sbcth |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbcth.1 |
. . 3
| |
| 2 | 1 | ax-gen 1622 |
. 2
|
| 3 | a4sbc 2734 |
. 2
| |
| 4 | 2, 3 | mpi 101 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: sbcth2 2780 csbeq2i 2826 iota4an 5275 bnj895 13742 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-gen 1622 ax-12 1627 ax-17 1634 ax-4 1637 ax-5o 1639 ax-6o 1642 ax-9o 1792 ax-ext 2152 |
| This theorem depends on definitions: df-bi 232 df-an 435 df-ex 1645 df-sb 1845 df-clab 2158 df-cleq 2163 df-clel 2166 df-v 2571 df-sbc 2731 |