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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
StepHypRef Expression
1 bi2 198 . . 3
2 bija.1 . . 3
31, 2syli 37 . 2
4 bi1 186 . . . 4
54con3d 133 . . 3
6 bija.2 . . 3
75, 6syli 37 . 2
83, 7pm2.61d 158 1
Colors of variables: wff setvar class
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
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