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Theorem jctild 299
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 → (θ χ)))

Proof of Theorem jctild
StepHypRef Expression
1 jctild.2 . . 3 (φθ)
21a1d 22 . 2 (φ → (ψθ))
3 jctild.1 . 2 (φ → (ψχ))
42, 3jcad 291 1 (φ → (ψ → (θ χ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101
This theorem is referenced by:  anc2li  312  syl6an  1320  poxp  5794  aptiprleml  6609  zmulcl  8033
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