New Foundations Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > NFE Home > Th. List > ifid | GIF version |
Description: Identical true and false arguments in the conditional operator. (Contributed by NM, 18-Apr-2005.) |
Ref | Expression |
---|---|
ifid | ⊢ if(φ, A, A) = A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iftrue 3668 | . 2 ⊢ (φ → if(φ, A, A) = A) | |
2 | iffalse 3669 | . 2 ⊢ (¬ φ → if(φ, A, A) = A) | |
3 | 1, 2 | pm2.61i 156 | 1 ⊢ if(φ, A, A) = A |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ifcif 3662 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-if 3663 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |