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Theorem 3imtr3g 260
 Description: More general version of 3imtr3i 256. Useful for converting definitions in a formula. (Contributed by NM, 20-May-1996.) (Proof shortened by Wolf Lammen, 20-Dec-2013.)
Hypotheses
Ref Expression
3imtr3g.1 (φ → (ψχ))
3imtr3g.2 (ψθ)
3imtr3g.3 (χτ)
Assertion
Ref Expression
3imtr3g (φ → (θτ))

Proof of Theorem 3imtr3g
StepHypRef Expression
1 3imtr3g.2 . . 3 (ψθ)
2 3imtr3g.1 . . 3 (φ → (ψχ))
31, 2syl5bir 209 . 2 (φ → (θχ))
4 3imtr3g.3 . 2 (χτ)
53, 4syl6ib 217 1 (φ → (θτ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177 This theorem is referenced by:  exim  1575  dvelimhw  1849  ax12olem2  1928  dvelimh  1964  dvelimALT  2133  dvelimf-o  2180  axi11e  2332  sspwb  4118  pw1disj  4167  ssopab2b  4713  imadif  5171  enpw1  6062
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