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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  3951  opeqex  4245  rabxfrd  4465  eqbrrdv  4719  eqbrrdiv  4720  opelco2g  4790  opelcnvg  4802  ralrnmpt  5653  rexrnmpt  5654  fliftcnv  5789  eusvobj2  5854  f1od2  6229  ottposg  6249  ercnv  6549  exmidpw  6901  djuf1olem  7045  fzen  10016  fihasheq0  10744  divalgb  11900  isprm3  12088  eldvap  13784
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