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Mirrors > Home > MPE Home > Th. List > breq123d | Structured version Visualization version Unicode version |
Description: Equality deduction for a binary relation. (Contributed by NM, 29-Oct-2011.) |
Ref | Expression |
---|---|
breq1d.1 | |
breq123d.2 | |
breq123d.3 |
Ref | Expression |
---|---|
breq123d |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1d.1 | . . 3 | |
2 | breq123d.3 | . . 3 | |
3 | 1, 2 | breq12d 4666 | . 2 |
4 | breq123d.2 | . . 3 | |
5 | 4 | breqd 4664 | . 2 |
6 | 3, 5 | bitrd 268 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 class class class wbr 4653 |
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-3an 1039 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-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-br 4654 |
This theorem is referenced by: sbcbr123 4706 fmptco 6396 xpsle 16241 invfuc 16634 yonedainv 16921 opphllem3 25641 lmif 25677 islmib 25679 iscgra 25701 isinag 25729 fmptcof2 29457 submomnd 29710 sgnsv 29727 inftmrel 29734 isinftm 29735 submarchi 29740 suborng 29815 uncov 33390 iscvlat 34610 paddfval 35083 lhpset 35281 tendofset 36046 diaffval 36319 fnwe2val 37619 aomclem8 37631 |
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