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Mirrors > Home > MPE Home > Th. List > eqfnov2 | Structured version Visualization version Unicode version |
Description: Two operators with the same domain are equal iff their values at each point in the domain are equal. (Contributed by Jeff Madsen, 7-Jun-2010.) |
Ref | Expression |
---|---|
eqfnov2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqfnov 6766 | . 2 | |
2 | simpr 477 | . . 3 | |
3 | eqidd 2623 | . . . 4 | |
4 | 3 | ancri 575 | . . 3 |
5 | 2, 4 | impbii 199 | . 2 |
6 | 1, 5 | syl6bb 276 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wral 2912 cxp 5112 wfn 5883 (class class class)co 6650 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ov 6653 |
This theorem is referenced by: fnmpt2ovd 7252 tpossym 7384 uncfcurf 16879 mamuass 20208 mamudi 20209 mamudir 20210 mamuvs1 20211 mamuvs2 20212 eqmat 20230 mamulid 20247 mamurid 20248 madutpos 20448 ressprdsds 22176 isngp3 22402 xrsdsre 22613 hhip 28034 1smat1 29870 matunitlindflem2 33406 |
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