Theorem 3an1rs 1209

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 114	. . . . 5 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3	2	3exp 1192	. . . 4 |- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
4	3	com34 83	. . 3 |- ( ph -> ( ps -> ( th -> ( ch -> ta ) ) ) )
5	4	3imp 1183	. 2 |- ( ( ph /\ ps /\ th ) -> ( ch -> ta ) )
6	5	imp 123	1 |- ( ( ( ph /\ ps /\ th ) /\ ch ) -> ta )

Syntax hints:   -> wi 4   /\ wa 103   /\ w3a 968

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116  df-3an 970

This theorem is referenced by: (None)