Theorem com24 87

Description: Commutation of antecedents. Swap 2nd and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)

Hypothesis

Ref	Expression
com4.1	|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Assertion

Ref	Expression
com24	|- ( ph -> ( th -> ( ch -> ( ps -> ta ) ) ) )

Proof of Theorem com24

Step	Hyp	Ref	Expression
1		com4.1	. . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2	1	com4t 85	. 2 |- ( ch -> ( th -> ( ph -> ( ps -> ta ) ) ) )
3	2	com13 80	1 |- ( ph -> ( th -> ( ch -> ( ps -> ta ) ) ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  com25  91  tfrlem9  6528  nnmordi  6727  fundmen  7024  fiintim  7166  elfzodifsumelfzo  10490  ssfzo12  10513  swrdswrdlem  11332  swrdswrd  11333  wrd2ind  11351  swrdccatin1  11353  dvdsmodexp  12417  dvdsaddre2b  12463  infpnlem1  12993  grpinveu  13682  mulgass2  14133  lss1d  14459  cnpnei  15010  clwwlkccatlem  16321