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Mirrors > Home > NFE Home > Th. List > cnveqi | GIF version |
Description: Equality inference for converse. (Contributed by set.mm contributors, 23-Dec-2008.) |
Ref | Expression |
---|---|
cnveqi.1 | ⊢ A = B |
Ref | Expression |
---|---|
cnveqi | ⊢ ◡A = ◡B |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnveqi.1 | . 2 ⊢ A = B | |
2 | cnveq 4886 | . 2 ⊢ (A = B → ◡A = ◡B) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ◡A = ◡B |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1642 ◡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: cnvin 5035 cnvxp 5043 xp0 5044 cnvtr 5098 fun11iun 5305 mptpreima 5682 f1od 5726 cnvpprod 5841 scancan 6331 |
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