Theorem dfixp 7491

Description: Eliminate the expression in df-ixp 7490, under the assumption that and are disjoint. This way, we can say that is bound in even if it appears free in . (Contributed by Mario Carneiro, 12-Aug-2016.)

Assertion

Ref	Expression
dfixp

Distinct variable groups:   ,,   ,   ,

Proof of Theorem dfixp

Step	Hyp	Ref	Expression
1		df-ixp 7490	. 2
2		abid2 2597	. . . . 5
3	2	fneq2i 5681	. . . 4
4	3	anbi1i 695	. . 3
5	4	abbii 2591	. 2
6	1, 5	eqtri 2486	1

Syntax hints:  /\wa 369  =wceq 1395  e.wcel 1818  {cab 2442  A.wral 2807  Fnwfn 5588  `cfv 5593  X_cixp 7489

This theorem is referenced by:  ixpsnval  7492  elixp2  7493  ixpeq1  7500  cbvixp  7506  ixp0x  7517

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-fn 5596  df-ixp 7490