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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1234 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj60 31130. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1234.2 | |
bnj1234.3 | |
bnj1234.4 | |
bnj1234.5 |
Ref | Expression |
---|---|
bnj1234 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fneq1 5979 | . . . . 5 | |
2 | fveq1 6190 | . . . . . . 7 | |
3 | reseq1 5390 | . . . . . . . . . 10 | |
4 | 3 | opeq2d 4409 | . . . . . . . . 9 |
5 | bnj1234.2 | . . . . . . . . 9 | |
6 | bnj1234.4 | . . . . . . . . 9 | |
7 | 4, 5, 6 | 3eqtr4g 2681 | . . . . . . . 8 |
8 | 7 | fveq2d 6195 | . . . . . . 7 |
9 | 2, 8 | eqeq12d 2637 | . . . . . 6 |
10 | 9 | ralbidv 2986 | . . . . 5 |
11 | 1, 10 | anbi12d 747 | . . . 4 |
12 | 11 | rexbidv 3052 | . . 3 |
13 | 12 | cbvabv 2747 | . 2 |
14 | bnj1234.3 | . 2 | |
15 | bnj1234.5 | . 2 | |
16 | 13, 14, 15 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wa 384 wceq 1483 cab 2608 wral 2912 wrex 2913 cop 4183 cres 5116 wfn 5883 cfv 5888 c-bnj14 30754 |
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-ral 2917 df-rex 2918 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-uni 4437 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-res 5126 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 |
This theorem is referenced by: bnj1245 31082 bnj1256 31083 bnj1259 31084 bnj1296 31089 bnj1311 31092 |
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