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Mirrors > Home > NFE Home > Th. List > cnveq | Unicode version |
Description: Equality theorem for converse. (Contributed by set.mm contributors, 13-Aug-1995.) |
Ref | Expression |
---|---|
cnveq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnvss 4885 | . . 3 | |
2 | cnvss 4885 | . . 3 | |
3 | 1, 2 | anim12i 549 | . 2 |
4 | eqss 3287 | . 2 | |
5 | eqss 3287 | . 2 | |
6 | 3, 4, 5 | 3imtr4i 257 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 358 wceq 1642 wss 3257 ccnv 4771 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-ss 3259 df-opab 4623 df-br 4640 df-cnv 4785 |
This theorem is referenced by: cnveqi 4887 cnveqd 4888 cnveqb 5063 funcnvuni 5161 f1eq1 5253 f1o00 5317 enprmaplem3 6078 enprmaplem5 6080 enprmaplem6 6081 |
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