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Theorem bitr2d 178
Description: Deduction form of bitr2i 174. (Contributed by NM, 9-Jun-2004.)
Hypotheses
Ref Expression
bitr2d.1 (φ → (ψχ))
bitr2d.2 (φ → (χθ))
Assertion
Ref Expression
bitr2d (φ → (θψ))

Proof of Theorem bitr2d
StepHypRef Expression
1 bitr2d.1 . . 3 (φ → (ψχ))
2 bitr2d.2 . . 3 (φ → (χθ))
31, 2bitrd 177 . 2 (φ → (ψθ))
43bicomd 129 1 (φ → (θψ))
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:  3bitrrd  204  3bitr2rd  206  pm5.18dc  776  drex1  1676  elrnmpt1  4528  xpopth  5744  sbcopeq1a  5755  ltaddsub  7206  leaddsub  7208  posdif  7225  lesub1  7226  ltsub1  7228  lesub0  7249  ltdivmul  7603  ledivmul  7604  zlem1lt  8056  zltlem1  8057  fzrev2  8697  fz1sbc  8708  elfzp1b  8709  sumsqeq0  8965
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