Theorem e3 16605

Description: Meta-connective form of syl8 27.

Hypotheses

Ref	Expression
e3.1	|- . ph, ps, ch   ⊢   th .
e3.2	|- (th -> ta)

Assertion

Ref	Expression
e3	|- . ph, ps, ch   ⊢   ta .

Proof of Theorem e3

Step	Hyp	Ref	Expression
1		e3.1	. 2 |- . ph, ps, ch   ⊢   th .
2		e3.2	. . 3 |- (th -> ta)
3	2	a1i 8	. 2 |- (th -> (th -> ta))
4	1, 1, 3	e33 16602	1 |- . ph, ps, ch   ⊢   ta .

Syntax hints:   -> wi 3   . vd3 16493

This theorem is referenced by:  e3bi 16606  e3bir 16607  truniALTVD 16702

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 164  df-an 242  df-3an 860  df-vd3 16494

Copyright terms: Public domain