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Theorem 3imtr4d 259
 Description: More general version of 3imtr4i 257. Useful for converting conditional definitions in a formula. (Contributed by NM, 26-Oct-1995.)
Hypotheses
Ref Expression
3imtr4d.1 (φ → (ψχ))
3imtr4d.2 (φ → (θψ))
3imtr4d.3 (φ → (τχ))
Assertion
Ref Expression
3imtr4d (φ → (θτ))

Proof of Theorem 3imtr4d
StepHypRef Expression
1 3imtr4d.2 . 2 (φ → (θψ))
2 3imtr4d.1 . . 3 (φ → (ψχ))
3 3imtr4d.3 . . 3 (φ → (τχ))
42, 3sylibrd 225 . 2 (φ → (ψτ))
51, 4sylbid 206 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:  ax11indalem  2197  ax11inda2ALT  2198  leltfintr  4458  ltfintr  4459  ltfintri  4466  ltlefin  4468  tfinltfinlem1  4500  vfinspsslem1  4550  pw1fnf1o  5855  enprmaplem3  6078  nchoicelem9  6297
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