NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  imim1i GIF version

Theorem imim1i 54
Description: Inference adding common consequents in an implication, thereby interchanging the original antecedent and consequent. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 4-Aug-2012.)
Hypothesis
Ref Expression
imim1i.1 (φψ)
Assertion
Ref Expression
imim1i ((ψχ) → (φχ))

Proof of Theorem imim1i
StepHypRef Expression
1 imim1i.1 . 2 (φψ)
2 id 19 . 2 (χχ)
31, 2imim12i 53 1 ((ψχ) → (φχ))
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by:  jarr  91  impt  149  jarl  155  bi3ant  280  pm2.67-2  391  pm3.41  542  pm3.42  543  jaob  758  3jaob  1244  merco1  1478  19.39  1661  19.23hOLD  1820  ax12olem3  1929  r19.37  2760
  Copyright terms: Public domain W3C validator