Theorem 2sb6 2188

Description: Equivalence for double substitution. (Contributed by NM, 3-Feb-2005.)

Assertion

Ref	Expression
2sb6

Distinct variable groups:   ,,   ,

Proof of Theorem 2sb6

Step	Hyp	Ref	Expression
1		sb6 2173	. 2
2		19.21v 1729	. . . 4
3		impexp 446	. . . . 5
4	3	albii 1640	. . . 4
5		sb6 2173	. . . . 5
6	5	imbi2i 312	. . . 4
7	2, 4, 6	3bitr4ri 278	. . 3
8	7	albii 1640	. 2
9	1, 8	bitri 249	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  [wsb 1739

This theorem is referenced by:  sbcom2  2189  2exsb  2213  2moOLD  2374  2eu6  2383  2eu6OLD  2384

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-12 1854  ax-13 1999

This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740