Theorem e33 16602

Description: A virtual deduction elimination rule.

Hypotheses

Ref	Expression
e33.1	|- . ph, ps, ch   ⊢   th .
e33.2	|- . ph, ps, ch   ⊢   ta .
e33.3	|- (th -> (ta -> et))

Assertion

Ref	Expression
e33	|- . ph, ps, ch   ⊢   et .

Proof of Theorem e33

Step	Hyp	Ref	Expression
1		e33.1	. 2 |- . ph, ps, ch   ⊢   th .
2		e33.2	. 2 |- . ph, ps, ch   ⊢   ta .
3		e33.3	. . 3 |- (th -> (ta -> et))
4	3	a1i 8	. 2 |- (th -> (th -> (ta -> et)))
5	1, 1, 2, 4	e333 16601	1 |- . ph, ps, ch   ⊢   et .

Syntax hints:   -> wi 3   . vd3 16493

This theorem is referenced by:  e33an 16603  e3 16605  e03 16608  e30 16612  e13 16616  e31 16619  e23 16623  e32 16626  truniALTVD 16702  trintALTVD 16704

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