Theorem 2euswap 2370

Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by NM, 10-Apr-2004.)

Assertion

Ref	Expression
2euswap

Proof of Theorem 2euswap

Step	Hyp	Ref	Expression
1		excomim 1850	. . . 4
2	1	a1i 11	. . 3
3		2moswap 2369	. . 3
4	2, 3	anim12d 563	. 2
5		eu5 2310	. 2
6		eu5 2310	. 2
7	4, 5, 6	3imtr4g 270	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  E.wex 1612  E!weu 2282  E*wmo 2283

This theorem is referenced by:  2eu1  2376  euxfr2  3284  2reuswap  3302  2reuswap2  27387

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

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287