Theorem sb3an 2141

Description: Conjunction inside and outside of a substitution are equivalent. (Contributed by NM, 14-Dec-2006.)

Assertion

Ref	Expression
sb3an

Proof of Theorem sb3an

Step	Hyp	Ref	Expression
1		df-3an 975	. . 3
2	1	sbbii 1746	. 2
3		sban 2140	. 2
4		sban 2140	. . . 4
5	4	anbi1i 695	. . 3
6		df-3an 975	. . 3
7	5, 6	bitr4i 252	. 2
8	2, 3, 7	3bitri 271	1

Syntax hints:  <->wb 184  /\wa 369  /\w3a 973  [wsb 1739

This theorem is referenced by:  sbc3angOLD  3391

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-or 370  df-an 371  df-3an 975  df-ex 1613  df-nf 1617  df-sb 1740