Theorem sylibrd 225

Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994.)

Hypotheses

Ref	Expression
sylibrd.1	|- (ph -> (ps -> ch))
sylibrd.2	|- (ph -> (th <-> ch))

Assertion

Ref	Expression
sylibrd	|- (ph -> (ps -> th))

Proof of Theorem sylibrd

Step	Hyp	Ref	Expression
1		sylibrd.1	. 2 |- (ph -> (ps -> ch))
2		sylibrd.2	. . 3 |- (ph -> (th <-> ch))
3	2	biimprd 214	. 2 |- (ph -> (ch -> th))
4	1, 3	syld 40	1 |- (ph -> (ps -> th))

Syntax hints:   -> wi 4   <-> wb 176

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

This theorem is referenced by:  3imtr4d  259  sbciegft  3077  eqsbc2  3104  fconstfv  5457  nmembers1  6272  nchoicelem12  6301