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Mirrors > Home > NFE Home > Th. List > imaeq1 | Unicode version |
Description: Equality theorem for image. (Contributed by set.mm contributors, 14-Aug-1994.) |
Ref | Expression |
---|---|
imaeq1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 4641 | . . . 4 | |
2 | 1 | rexbidv 2635 | . . 3 |
3 | 2 | abbidv 2467 | . 2 |
4 | df-ima 4727 | . 2 | |
5 | df-ima 4727 | . 2 | |
6 | 3, 4, 5 | 3eqtr4g 2410 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1642 cab 2339 wrex 2615 class class class wbr 4639 cima 4722 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-rex 2620 df-br 4640 df-ima 4727 |
This theorem is referenced by: imaeq1i 4939 imaeq1d 4941 rneq 4956 f1imacnv 5302 clos1eq2 5875 eceq2 5963 |
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