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  6386  nnmordi  6583  fundmen  6874  fiintim  7001  elfzodifsumelfzo  10294  ssfzo12  10317  dvdsmodexp  11977  dvdsaddre2b  12023  infpnlem1  12553  grpinveu  13240  mulgass2  13690  lss1d  14015  cnpnei  14539