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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 (𝜑 → (𝜓𝜒))
jctild.2 (𝜑𝜃)
Assertion
Ref Expression
jctild (𝜑 → (𝜓 → (𝜃𝜒)))

Proof of Theorem jctild
StepHypRef Expression
1 jctild.2 . . 3 (𝜑𝜃)
21a1d 22 . 2 (𝜑 → (𝜓𝜃))
3 jctild.1 . 2 (𝜑 → (𝜓𝜒))
42, 3jcad 301 1 (𝜑 → (𝜓 → (𝜃𝜒)))
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  5904  aptiprleml  6943  zmulcl  8537  rexuz3  10077  cau3lem  10201  gcdzeq  10618  isprm3  10707
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