Theorem 3expd 850

Description: Exportation deduction for triple conjunction.

Hypothesis

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

Assertion

Ref	Expression
3expd	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem 3expd

Step	Hyp	Ref	Expression
1		3expd.1	. . . 4 |- (ph -> ((ps /\ ch /\ th) -> ta))
2	1	com12 11	. . 3 |- ((ps /\ ch /\ th) -> (ph -> ta))
3	2	3exp 832	. 2 |- (ps -> (ch -> (th -> (ph -> ta))))
4	3	com4r 41	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 3   /\ w3a 775

This theorem is referenced by:  3exp2 851  mulcant 5690  psdmrn 8648  psref 8649  and4com 10433  filint2 10574  filint2OLD 10575  efilcp2 10581  efilcp2OLD 10582  cnfilca 10583  cnfilcaOLD 10584  cmpmon 10743

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 777

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