Theorem syl6mpi 58

Description: e20 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof shortened by Wolf Lammen, 13-Sep-2012.)

Hypotheses

Ref	Expression
syl6mpi.1	|- (ph -> (ps -> ch))
syl6mpi.2	|- th
syl6mpi.3	|- (ch -> (th -> ta))

Assertion

Ref	Expression
syl6mpi	|- (ph -> (ps -> ta))

Proof of Theorem syl6mpi

Step	Hyp	Ref	Expression
1		syl6mpi.1	. 2 |- (ph -> (ps -> ch))
2		syl6mpi.2	. . 3 |- th
3		syl6mpi.3	. . 3 |- (ch -> (th -> ta))
4	2, 3	mpi 16	. 2 |- (ch -> ta)
5	1, 4	syl6 29	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)