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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  1280  sbal2  1895  eqsnm  3517  fnressn  5292  fressnfv  5293  eluniimadm  5347  genpassl  6506  genpassu  6507  1idprl  6565  1idpru  6566  negeq0  7041  muleqadd  7411  crap0  7671  addltmul  7918  fzrev  8696  cjap0  9115  cjne0  9116  elabgf0  9231
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