Theorem 3an1rs 843

Description: Swap conjuncts.

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 373	. . . . 5 |- ((ph /\ ps /\ ch) -> (th -> ta))
3	2	3exp 830	. . . 4 |- (ph -> (ps -> (ch -> (th -> ta))))
4	3	com34 36	. . 3 |- (ph -> (ps -> (th -> (ch -> ta))))
5	4	3imp 825	. 2 |- ((ph /\ ps /\ th) -> (ch -> ta))
6	5	imp 350	1 |- (((ph /\ ps /\ th) /\ ch) -> ta)

Syntax hints:   -> wi 3   /\ wa 223   /\ w3a 773

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225  df-3an 775

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