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Theorem jctird 317
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 307 1 (𝜑 → (𝜓 → (𝜒𝜃)))
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108
This theorem is referenced by:  anc2ri  330  ordunisuc2r  4515  fnun  5324  fco  5383  fiintim  6930  cauappcvgprlemladdru  7657  cauappcvgprlemladdrl  7658  caucvgprlemnkj  7667  dvdsdivcl  11858  cnrest2  13821  cnptopresti  13823  bdxmet  14086  lgsdir  14521
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