Theorem sbbid 2144

Description: Deduction substituting both sides of a biconditional. (Contributed by NM, 30-Jun-1993.)

Hypotheses

Ref	Expression
sbbid.1
sbbid.2

Assertion

Ref	Expression
sbbid

Proof of Theorem sbbid

Step	Hyp	Ref	Expression
1		sbbid.1	. . 3
2		sbbid.2	. . 3
3	1, 2	alrimi 1877	. 2
4		spsbbi 2143	. 2
5	3, 4	syl 16	1

Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739

This theorem is referenced by:  sbcom3  2153  sbco3  2160  sbcom2  2189  sbal  2206  wl-equsb3  30004  wl-sbcom2d-lem1  30009  wl-sbcom3  30035

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-ex 1613  df-nf 1617  df-sb 1740