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Mirrors > Home > MPE Home > Th. List > ifeqor | Unicode version |
Description: The possible values of a conditional operator. (Contributed by NM, 17-Jun-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
ifeqor |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iftrue 3947 | . . . 4 | |
2 | 1 | con3i 135 | . . 3 |
3 | 2 | iffalsed 3952 | . 2 |
4 | 3 | orri 376 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -. wn 3 \/ wo 368
= wceq 1395 if cif 3941 |
This theorem is referenced by: ifpr 4077 rabrsn 4100 muval2 23408 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-11 1842 ax-12 1854 ax-13 1999 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-sb 1740 df-clab 2443 df-cleq 2449 df-clel 2452 df-if 3942 |
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