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Mirrors > Home > MPE Home > Th. List > Mathboxes > ifnmfalse | Structured version Visualization version Unicode version |
Description: If A is not a member of B, but an "if" condition requires it, then the "false" branch results. This is a simple utility to provide a slight shortening and simplification of proofs vs. applying iffalse 4095 directly in this case. (Contributed by David A. Wheeler, 15-May-2015.) |
Ref | Expression |
---|---|
ifnmfalse |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nel 2898 | . 2 | |
2 | iffalse 4095 | . 2 | |
3 | 1, 2 | sylbi 207 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wceq 1483 wcel 1990 wnel 2897 cif 4086 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nel 2898 df-if 4087 |
This theorem is referenced by: (None) |
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