Theorem 3an1rs 1163

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 423	. . . . 5 |- ((ph /\ ps /\ ch) -> (th -> ta))
3	2	3exp 1150	. . . 4 |- (ph -> (ps -> (ch -> (th -> ta))))
4	3	com34 77	. . 3 |- (ph -> (ps -> (th -> (ch -> ta))))
5	4	3imp 1145	. 2 |- ((ph /\ ps /\ th) -> (ch -> ta))
6	5	imp 418	1 |- (((ph /\ ps /\ th) /\ ch) -> ta)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by: (None)