Theorem 3an1rs 1279

Description: Swap conjuncts. (Contributed by NM, 16-Dec-2007.)

Hypothesis

Ref	Expression
3an1rs.1	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
3an1rs	|- ( ( ( ph /\ ps /\ th ) /\ ch ) -> ta )

Proof of Theorem 3an1rs

Step	Hyp	Ref	Expression
1		3an1rs.1	. . . . . 6 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
2	1	ex 450	. . . . 5 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3	2	3exp 1264	. . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	com34 91	. . 3 |- ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) )
5	4	3imp 1256	. 2 |- ( ( ph /\ ps /\ th ) -> ( ch -> ta ) )
6	5	imp 445	1 |- ( ( ( ph /\ ps /\ th ) /\ ch ) -> ta )

Syntax hints:   -> wi 4   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by:  odf1o2  17988  neiptopnei  20936  cnextcn  21871