Theorem ee21 1375

Description: e21 in set.mm without virtual deductions. (Contributed by Alan Sare, 18-Mar-2012.) (New usage is discouraged.) TODO: decide if this is worth keeping.

Hypotheses

Ref	Expression
ee21.1	|- (ph -> (ps -> ch))
ee21.2	|- (ph -> th)
ee21.3	|- (ch -> (th -> ta))

Assertion

Ref	Expression
ee21	|- (ph -> (ps -> ta))

Proof of Theorem ee21

Step	Hyp	Ref	Expression
1		ee21.1	. 2 |- (ph -> (ps -> ch))
2		ee21.2	. . 3 |- (ph -> th)
3	2	a1d 22	. 2 |- (ph -> (ps -> th))
4		ee21.3	. 2 |- (ch -> (th -> ta))
5	1, 3, 4	ee22 1362	1 |- (ph -> (ps -> ta))

Syntax hints:   -> wi 4

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

This theorem is referenced by: (None)