Theorem vd03 16500

Description: A theorem is virtually inferred by the 3 virtual hypotheses.

Hypothesis

Ref	Expression
vd03.1	|- ph

Assertion

Ref	Expression
vd03	|- . ps, ch, th   ⊢   ph .

Proof of Theorem vd03

Step	Hyp	Ref	Expression
1		vd03.1	. . . . 5 |- ph
2	1	a1i 8	. . . 4 |- (th -> ph)
3	2	a1i 8	. . 3 |- (ch -> (th -> ph))
4	3	a1i 8	. 2 |- (ps -> (ch -> (th -> ph)))
5	4	dfvd3ir 16497	1 |- . ps, ch, th   ⊢   ph .

Syntax hints:   -> wi 3   . vd3 16493

This theorem is referenced by:  e03 16608  e30 16612

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