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Mirrors > Home > MPE Home > Th. List > ifeq2 | Structured version Visualization version Unicode version |
Description: Equality theorem for conditional operator. (Contributed by NM, 1-Sep-2004.) (Revised by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
ifeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeq 3192 | . . 3 | |
2 | 1 | uneq2d 3767 | . 2 |
3 | dfif6 4089 | . 2 | |
4 | dfif6 4089 | . 2 | |
5 | 2, 3, 4 | 3eqtr4g 2681 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wceq 1483 crab 2916 cun 3572 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: ifeq12 4103 ifeq2d 4105 ifbieq2i 4110 ifexg 4157 somincom 5530 mdetunilem9 20426 prmorcht 24904 pclogsum 24940 noeta 31868 matunitlindflem1 33405 ftc1anclem6 33490 ftc1anclem8 33492 ftc1anc 33493 hdmap1cbv 37092 hoidmv1le 40808 hoidmvlelem3 40811 vonn0ioo 40901 vonn0icc 40902 |
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