Theorem sylan2d 468

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

Hypotheses

Ref	Expression
sylan2d.1	|- (ph -> (ps -> ch))
sylan2d.2	|- (ph -> ((th /\ ch) -> ta))

Assertion

Ref	Expression
sylan2d	|- (ph -> ((th /\ ps) -> ta))

Proof of Theorem sylan2d

Step	Hyp	Ref	Expression
1		sylan2d.1	. . 3 |- (ph -> (ps -> ch))
2		sylan2d.2	. . . 4 |- (ph -> ((th /\ ch) -> ta))
3	2	ancomsd 440	. . 3 |- (ph -> ((ch /\ th) -> ta))
4	1, 3	syland 467	. 2 |- (ph -> ((ps /\ th) -> ta))
5	4	ancomsd 440	1 |- (ph -> ((th /\ ps) -> ta))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  syl2and  469  sylan2i  636