Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj62 | Structured version Visualization version Unicode version |
Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj62 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vex 3203 | . . . 4 | |
2 | fneq1 5979 | . . . 4 | |
3 | 1, 2 | sbcie 3470 | . . 3 |
4 | 3 | sbcbii 3491 | . 2 |
5 | sbcco 3458 | . 2 | |
6 | vex 3203 | . . 3 | |
7 | fneq1 5979 | . . 3 | |
8 | 6, 7 | sbcie 3470 | . 2 |
9 | 4, 5, 8 | 3bitr3i 290 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wsbc 3435 wfn 5883 |
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-sbc 3436 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 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-fun 5890 df-fn 5891 |
This theorem is referenced by: bnj156 30796 bnj976 30848 bnj581 30978 |
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