Theorem syland 467

Description: A syllogism deduction. (Contributed by NM, 15-Dec-2004.)

Hypotheses

Ref	Expression
syland.1	|- (ph -> (ps -> ch))
syland.2	|- (ph -> ((ch /\ th) -> ta))

Assertion

Ref	Expression
syland	|- (ph -> ((ps /\ th) -> ta))

Proof of Theorem syland

Step	Hyp	Ref	Expression
1		syland.1	. . 3 |- (ph -> (ps -> ch))
2		syland.2	. . . 4 |- (ph -> ((ch /\ th) -> ta))
3	2	exp3a 425	. . 3 |- (ph -> (ch -> (th -> ta)))
4	1, 3	syld 40	. 2 |- (ph -> (ps -> (th -> ta)))
5	4	imp3a 420	1 |- (ph -> ((ps /\ th) -> ta))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  sylan2d  468  syl2and  469  sylani  635