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Mirrors > Home > MPE Home > Th. List > ifeq1 | 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 |
---|---|
ifeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rabeq 3192 | . . 3 | |
2 | 1 | uneq1d 3766 | . 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 ifeq1d 4104 ifbieq12i 4112 ifexg 4157 rdgeq2 7508 dfoi 8416 wemaplem2 8452 cantnflem1 8586 prodeq2w 14642 prodeq2ii 14643 mgm2nsgrplem2 17406 mgm2nsgrplem3 17407 mplcoe3 19466 marrepval0 20367 ellimc 23637 ply1nzb 23882 dchrvmasumiflem1 25190 signspval 30629 dfrdg2 31701 dfafv2 41212 |
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