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  10509  ssfzo12  10532  swrdswrdlem  11351  swrdswrd  11352  wrd2ind  11370  swrdccatin1  11372  dvdsmodexp  12436  dvdsaddre2b  12482  infpnlem1  13012  grpinveu  13701  mulgass2  14152  lss1d  14479  cnpnei  15030  clwwlkccatlem  16341