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Theorem 3imtr3g 193
Description: More general version of 3imtr3i 189. 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 142 . 2 (φ → (θχ))
4 3imtr3g.3 . 2 (χτ)
53, 4syl6ib 150 1 (φ → (θτ))
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:  dvelimfALT2  1695  dvelimf  1888  dveeq1  1892  sspwb  3943  ssopab2b  4004  imadif  4922  ssoprab2b  5504  iinerm  6114  uzind  8125
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