Theorem sylanr2 463

Description: A syllogism inference.

Hypotheses

Ref	Expression
sylanr2.1	|- ((ph /\ (ps /\ ch)) -> th)
sylanr2.2	|- (ta -> ch)

Assertion

Ref	Expression
sylanr2	|- ((ph /\ (ps /\ ta)) -> th)

Proof of Theorem sylanr2

Step	Hyp	Ref	Expression
1		sylanr2.1	. 2 |- ((ph /\ (ps /\ ch)) -> th)
2		sylanr2.2	. . 3 |- (ta -> ch)
3	2	anim2i 335	. 2 |- ((ps /\ ta) -> (ps /\ ch))
4	1, 3	sylan2 451	1 |- ((ph /\ (ps /\ ta)) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  mulsubt 5457  fzsubelt 6441  climsub 7074  iserzcmp 7086  iserzcmp0 7087  caucvglem6 7106  tgclt 7574  irredlem4 10257

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain