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Mirrors > Home > ILE Home > Th. List > ifnefalse | Unicode version |
Description: When values are unequal, but an "if" condition checks if they are equal, then the "false" branch results. This is a simple utility to provide a slight shortening and simplification of proofs versus applying iffalse 3523 directly in this case. (Contributed by David A. Wheeler, 15-May-2015.) |
Ref | Expression |
---|---|
ifnefalse |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ne 2335 | . 2 | |
2 | iffalse 3523 | . 2 | |
3 | 1, 2 | sylbi 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wceq 1342 wne 2334 cif 3515 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-11 1493 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-ne 2335 df-if 3516 |
This theorem is referenced by: xnegmnf 9756 rexneg 9757 xaddpnf1 9773 xaddpnf2 9774 xaddmnf1 9775 xaddmnf2 9776 mnfaddpnf 9778 rexadd 9779 fztpval 10008 pcval 12207 |
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