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Theorem 3imtr3g 203
Description: More general version of 3imtr3i 199. 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 152 . 2 (𝜑 → (𝜃𝜒))
4 3imtr3g.3 . 2 (𝜒𝜏)
53, 4syl6ib 160 1 (𝜑 → (𝜃𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  dvelimfALT2  1789  dvelimf  1990  dveeq1  1994  sspwb  4138  ssopab2b  4198  wetrep  4282  imadif  5203  ssoprab2b  5828  iinerm  6501  uzind  9174  bezoutlembi  11704
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