Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > fnunsn | Structured version Visualization version Unicode version |
Description: Extension of a function with a new ordered pair. (Contributed by NM, 28-Sep-2013.) (Revised by Mario Carneiro, 30-Apr-2015.) |
Ref | Expression |
---|---|
fnunop.x | |
fnunop.y | |
fnunop.f | |
fnunop.g | |
fnunop.e | |
fnunop.d |
Ref | Expression |
---|---|
fnunsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnunop.f | . . 3 | |
2 | fnunop.x | . . . 4 | |
3 | fnunop.y | . . . 4 | |
4 | fnsng 5938 | . . . 4 | |
5 | 2, 3, 4 | syl2anc 693 | . . 3 |
6 | fnunop.d | . . . 4 | |
7 | disjsn 4246 | . . . 4 | |
8 | 6, 7 | sylibr 224 | . . 3 |
9 | fnun 5997 | . . 3 | |
10 | 1, 5, 8, 9 | syl21anc 1325 | . 2 |
11 | fnunop.g | . . . 4 | |
12 | 11 | fneq1i 5985 | . . 3 |
13 | fnunop.e | . . . 4 | |
14 | 13 | fneq2i 5986 | . . 3 |
15 | 12, 14 | bitri 264 | . 2 |
16 | 10, 15 | sylibr 224 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wceq 1483 wcel 1990 cvv 3200 cun 3572 cin 3573 c0 3915 csn 4177 cop 4183 wfn 5883 |
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 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
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-sn 4178 df-pr 4180 df-op 4184 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-fun 5890 df-fn 5891 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |