Theorem exp41 384

Description: An exportation inference.

Hypothesis

Ref	Expression
exp41.1	|- ((((ph /\ ps) /\ ch) /\ th) -> ta)

Assertion

Ref	Expression
exp41	|- (ph -> (ps -> (ch -> (th -> ta))))

Proof of Theorem exp41

Step	Hyp	Ref	Expression
1		exp41.1	. . 3 |- ((((ph /\ ps) /\ ch) /\ th) -> ta)
2	1	ex 373	. 2 |- (((ph /\ ps) /\ ch) -> (th -> ta))
3	2	exp31 378	1 |- (ph -> (ps -> (ch -> (th -> ta))))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  tz7.49 3965  supxrun 6087  ser1add2 6339  fsumsplit 7020  fsumrev 7029  climshft 7104  fsum0diag4 7261  infxpidmlem12 7564  iscncl 7767  bcthlem29 8024  osumlem4 9576  branmfnt 10033

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

Copyright terms: Public domain