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Theorem syl5rbbr 184
Description: A syllogism inference from two biconditionals. (Contributed by NM, 25-Nov-1994.)
Hypotheses
Ref Expression
syl5rbbr.1 (ψφ)
syl5rbbr.2 (χ → (ψθ))
Assertion
Ref Expression
syl5rbbr (χ → (θφ))

Proof of Theorem syl5rbbr
StepHypRef Expression
1 syl5rbbr.1 . . 3 (ψφ)
21bicomi 123 . 2 (φψ)
3 syl5rbbr.2 . 2 (χ → (ψθ))
42, 3syl5rbb 182 1 (χ → (θφ))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  xordc  1266  sbal2  1880  eqsnm  3500  fnressn  5274  fressnfv  5275  eluniimadm  5329  genpassl  6379  genpassu  6380  1idprl  6429  1idpru  6430  negeq0  6851  elabgf0  7023
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