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Theorem jctild 314
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 305 1  |-  ( ph  ->  ( ps  ->  ( th  /\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107
This theorem is referenced by:  anc2li  327  syl6an  1410  poxp  6129  ssenen  6745  aptiprleml  7454  zmulcl  9114  rexuz3  10769  cau3lem  10893  gcdzeq  11717  isprm3  11806  epttop  12269  lmtopcnp  12429  txcnp  12450
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