Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > resfunexgALT | Structured version Visualization version Unicode version |
Description: Alternate proof of resfunexg 6479, shorter but requiring ax-pow 4843 and ax-un 6949. (Contributed by NM, 7-Apr-1995.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
resfunexgALT |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmresexg 5421 | . . . 4 | |
2 | 1 | adantl 482 | . . 3 |
3 | df-ima 5127 | . . . 4 | |
4 | funimaexg 5975 | . . . 4 | |
5 | 3, 4 | syl5eqelr 2706 | . . 3 |
6 | 2, 5 | jca 554 | . 2 |
7 | xpexg 6960 | . 2 | |
8 | relres 5426 | . . . 4 | |
9 | relssdmrn 5656 | . . . 4 | |
10 | 8, 9 | ax-mp 5 | . . 3 |
11 | ssexg 4804 | . . 3 | |
12 | 10, 11 | mpan 706 | . 2 |
13 | 6, 7, 12 | 3syl 18 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wcel 1990 cvv 3200 wss 3574 cxp 5112 cdm 5114 crn 5115 cres 5116 cima 5117 wrel 5119 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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-fun 5890 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |