Theorem addex 9843

Description: The addition operation is a set. (Contributed by NM, 19-Oct-2004.) (Revised by Mario Carneiro, 17-Nov-2014.)

Assertion

Ref	Expression
addex	|- + e. _V

Proof of Theorem addex

Step	Hyp	Ref	Expression
1		ax-addf 8117	. 2 |- + : ( CC X. CC ) --> CC
2		cnex 8119	. . 3 |- CC e. _V
3	2, 2	xpex 4833	. 2 |- ( CC X. CC ) e. _V
4		fex2 5491	. 2 |- ( ( + : ( CC X. CC ) --> CC /\ ( CC X. CC ) e. _V /\ CC e. _V ) -> + e. _V )
5	1, 3, 2, 4	mp3an 1371	1 |- + e. _V

Syntax hints:   e. wcel 2200   _Vcvv 2799   X. cxp 4716   -->wf 5313   CCcc 7993   + caddc 7998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-13 2202  ax-14 2203  ax-ext 2211  ax-sep 4201  ax-pow 4257  ax-pr 4292  ax-un 4523  ax-cnex 8086  ax-addf 8117

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-pw 3651  df-sn 3672  df-pr 3673  df-op 3675  df-uni 3888  df-br 4083  df-opab 4145  df-xp 4724  df-rel 4725  df-cnv 4726  df-dm 4728  df-rn 4729  df-fun 5319  df-fn 5320  df-f 5321

This theorem is referenced by: (None)