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	|- (ph -> ps)

Assertion

Ref	Expression
imim1i	|- ((ps -> ch) -> (ph -> ch))

Proof of Theorem imim1i

Step	Hyp	Ref	Expression
1		imim1i.1	. 2 |- (ph -> ps)
2		id 19	. 2 |- (ch -> ch)
3	1, 2	imim12i 53	1 |- ((ps -> ch) -> (ph -> ch))

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  2761