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Theorem 3bitr3g 222
Description: More general version of 3bitr3i 210. Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995.)
Hypotheses
Ref Expression
3bitr3g.1 (𝜑 → (𝜓𝜒))
3bitr3g.2 (𝜓𝜃)
3bitr3g.3 (𝜒𝜏)
Assertion
Ref Expression
3bitr3g (𝜑 → (𝜃𝜏))

Proof of Theorem 3bitr3g
StepHypRef Expression
1 3bitr3g.2 . . 3 (𝜓𝜃)
2 3bitr3g.1 . . 3 (𝜑 → (𝜓𝜒))
31, 2bitr3id 194 . 2 (𝜑 → (𝜃𝜒))
4 3bitr3g.3 . 2 (𝜒𝜏)
53, 4bitrdi 196 1 (𝜑 → (𝜃𝜏))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 105
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  con2bidc  875  sbal1yz  2001  sbal1  2002  dfsbcq2  2965  iindif2m  3954  opeqex  4249  rabxfrd  4469  eqbrrdv  4723  eqbrrdiv  4724  opelco2g  4795  opelcnvg  4807  ralrnmpt  5658  rexrnmpt  5659  fliftcnv  5795  eusvobj2  5860  f1od2  6235  ottposg  6255  ercnv  6555  exmidpw  6907  djuf1olem  7051  fzen  10042  fihasheq0  10772  divalgb  11929  isprm3  12117  eldvap  14121
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