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Theorem jctird 310
Description: Deduction conjoining a theorem to right of consequent in an implication. (Contributed by NM, 21-Apr-2005.)
Hypotheses
Ref Expression
jctird.1 (𝜑 → (𝜓𝜒))
jctird.2 (𝜑𝜃)
Assertion
Ref Expression
jctird (𝜑 → (𝜓 → (𝜒𝜃)))

Proof of Theorem jctird
StepHypRef Expression
1 jctird.1 . 2 (𝜑 → (𝜓𝜒))
2 jctird.2 . . 3 (𝜑𝜃)
32a1d 22 . 2 (𝜑 → (𝜓𝜃))
41, 3jcad 301 1 (𝜑 → (𝜓 → (𝜒𝜃)))
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:  anc2ri  323  ordunisuc2r  4266  fnun  5036  fco  5087  cauappcvgprlemladdru  6908  cauappcvgprlemladdrl  6909  caucvgprlemnkj  6918  dvdsdivcl  10395
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