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Theorem jctild 309
Description: Deduction conjoining a theorem to left of consequent in an implication. (Contributed by NM, 21-Apr-2005.)
Hypotheses
Ref Expression
jctild.1  |-  ( ph  ->  ( ps  ->  ch ) )
jctild.2  |-  ( ph  ->  th )
Assertion
Ref Expression
jctild  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )

Proof of Theorem jctild
StepHypRef Expression
1 jctild.2 . . 3  |-  ( ph  ->  th )
21a1d 22 . 2  |-  ( ph  ->  ( ps  ->  th )
)
3 jctild.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3jcad 301 1  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106
This theorem is referenced by:  anc2li  322  syl6an  1364  poxp  5884  aptiprleml  6891  zmulcl  8485  rexuz3  10014  cau3lem  10138  gcdzeq  10555  isprm3  10644
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