Theorem bija 355

Description: Combine antecedents into a single biconditional. This inference, reminiscent of ja 161, is reversible: The hypotheses can be deduced from the conclusion alone (see pm5.1im 238 and pm5.21im 349). (Contributed by Wolf Lammen, 13-May-2013.)

Hypotheses

Ref	Expression
bija.1
bija.2

Assertion

Ref	Expression
bija

Proof of Theorem bija

Step	Hyp	Ref	Expression
1		bi2 198	. . 3
2		bija.1	. . 3
3	1, 2	syli 37	. 2
4		bi1 186	. . . 4
5	4	con3d 133	. . 3
6		bija.2	. . 3
7	5, 6	syli 37	. 2
8	3, 7	pm2.61d 158	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184

This theorem is referenced by:  equveli  2088  wl-aleq  29988  wl-nfeqfb  29990  bj-bibibi  34175  rp-fakeimass  37736  rp-fakenanass  37739

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185