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Mirrors > Home > MPE Home > Th. List > funeq | Structured version Visualization version Unicode version |
Description: Equality theorem for function predicate. (Contributed by NM, 16-Aug-1994.) |
Ref | Expression |
---|---|
funeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqimss2 3658 | . . 3 | |
2 | funss 5907 | . . 3 | |
3 | 1, 2 | syl 17 | . 2 |
4 | eqimss 3657 | . . 3 | |
5 | funss 5907 | . . 3 | |
6 | 4, 5 | syl 17 | . 2 |
7 | 3, 6 | impbid 202 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wceq 1483 wss 3574 wfun 5882 |
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-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-in 3581 df-ss 3588 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-fun 5890 |
This theorem is referenced by: funeqi 5909 funeqd 5910 fununi 5964 cnvresid 5968 fneq1 5979 funop 6414 funsndifnop 6416 nvof1o 6536 funcnvuni 7119 elpmg 7873 fundmeng 8031 isfsupp 8279 dfac9 8958 axdc3lem2 9273 frlmphllem 20119 usgredgop 26065 locfinreflem 29907 orvcval 30519 bnj1379 30901 bnj1385 30903 bnj1497 31128 elfunsg 32023 funop1 41302 |
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