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Theorem jccil 560
Description: Inference conjoining a consequent of a consequent to the left of the consequent in an implication. Remark: One can also prove this theorem using syl 17 and jca 552 (as done in jccir 559), which would be 4 bytes shorter, but one step longer than the current proof. (Proof modification is discouraged.) (Contributed by AV, 20-Aug-2019.)
Hypotheses
Ref Expression
jccir.1 (𝜑𝜓)
jccir.2 (𝜓𝜒)
Assertion
Ref Expression
jccil (𝜑 → (𝜒𝜓))

Proof of Theorem jccil
StepHypRef Expression
1 jccir.1 . . 3 (𝜑𝜓)
2 jccir.2 . . 3 (𝜓𝜒)
31, 2jccir 559 . 2 (𝜑 → (𝜓𝜒))
43ancomd 465 1 (𝜑 → (𝜒𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384
This theorem is referenced by:  inatsk  9456  relexpindlem  13599  el2wlksoton  26198  el2spthsoton  26199
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