Theorem mpt2v 6392

Description: Operation with universal domain in maps-to notation. (Contributed by NM, 16-Aug-2013.)

Assertion

Ref	Expression
mpt2v

Distinct variable groups:   ,   ,   ,

Proof of Theorem mpt2v

Step	Hyp	Ref	Expression
1		df-mpt2 6301	. 2
2		vex 3112	. . . . 5
3		vex 3112	. . . . 5
4	2, 3	pm3.2i 455	. . . 4
5	4	biantrur 506	. . 3
6	5	oprabbii 6352	. 2
7	1, 6	eqtr4i 2489	1

Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  cvv 3109  {coprab 6297  e.cmpt2 6298

This theorem is referenced by:  1st2val  6826  2nd2val  6827

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-oprab 6300  df-mpt2 6301