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  6374  nnmordi  6571  fundmen  6862  fiintim  6987  elfzodifsumelfzo  10271  ssfzo12  10294  dvdsmodexp  11941  dvdsaddre2b  11987  infpnlem1  12500  grpinveu  13113  mulgass2  13557  lss1d  13882  cnpnei  14398