MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  jccil Structured version   Visualization version   GIF version

Theorem jccil 523
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 512 (as done in jccir 522), 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 522 . 2 (𝜑 → (𝜓𝜒))
43ancomd 462 1 (𝜑 → (𝜒𝜓))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 396
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 208  df-an 397
This theorem is referenced by:  inatsk  10188  relexpindlem  14410
  Copyright terms: Public domain W3C validator