Theorem syl2and 469

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

Hypotheses

Ref	Expression
syl2and.1	|- (ph -> (ps -> ch))
syl2and.2	|- (ph -> (th -> ta))
syl2and.3	|- (ph -> ((ch /\ ta) -> et))

Assertion

Ref	Expression
syl2and	|- (ph -> ((ps /\ th) -> et))

Proof of Theorem syl2and

Step	Hyp	Ref	Expression
1		syl2and.1	. 2 |- (ph -> (ps -> ch))
2		syl2and.2	. . 3 |- (ph -> (th -> ta))
3		syl2and.3	. . 3 |- (ph -> ((ch /\ ta) -> et))
4	2, 3	sylan2d 468	. 2 |- (ph -> ((ch /\ th) -> et))
5	1, 4	syland 467	1 |- (ph -> ((ps /\ th) -> et))

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:  anim12d  546  tfin11  4494