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Mirrors > Home > MPE Home > Th. List > ifbieq2i | Structured version Visualization version Unicode version |
Description: Equivalence/equality inference for conditional operators. (Contributed by Paul Chapman, 22-Jun-2011.) |
Ref | Expression |
---|---|
ifbieq2i.1 | |
ifbieq2i.2 |
Ref | Expression |
---|---|
ifbieq2i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ifbieq2i.1 | . . 3 | |
2 | ifbi 4107 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | ifbieq2i.2 | . . 3 | |
5 | ifeq2 4091 | . . 3 | |
6 | 4, 5 | ax-mp 5 | . 2 |
7 | 3, 6 | eqtri 2644 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 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-nfc 2753 df-rab 2921 df-v 3202 df-un 3579 df-if 4087 |
This theorem is referenced by: ifbieq12i 4112 gcdcom 15235 gcdass 15264 lcmcom 15306 lcmass 15327 bj-xpimasn 32942 cdleme31sdnN 35675 cdlemefr44 35713 cdleme48fv 35787 cdlemeg49lebilem 35827 cdleme50eq 35829 hoidmvlelem3 40811 hoidmvlelem4 40812 |
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