Theorem 3imp2 846

Description: Importation to right triple conjunction.

Hypothesis

Ref	Expression
3imp1.1	|- (ph -> (ps -> (ch -> (th -> ta))))

Assertion

Ref	Expression
3imp2	|- ((ph /\ (ps /\ ch /\ th)) -> ta)

Proof of Theorem 3imp2

Step	Hyp	Ref	Expression
1		3imp1.1	. . 3 |- (ph -> (ps -> (ch -> (th -> ta))))
2	1	3impd 845	. 2 |- (ph -> ((ps /\ ch /\ th) -> ta))
3	2	imp 350	1 |- ((ph /\ (ps /\ ch /\ th)) -> ta)

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

This theorem is referenced by:  cnpimaex 7704  hausnei 7723  metcnpi 7829  metcnpi2 7830  metcnpi3 7831  metcnpi4 7832  grprcan 7997  grplcan 8010  and4com 10333  cmpmon 10585  icmpmon 10587

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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