Theorem sylanr1 462

Description: A syllogism inference.

Hypotheses

Ref	Expression
sylanr1.1	|- ((ph /\ (ps /\ ch)) -> th)
sylanr1.2	|- (ta -> ps)

Assertion

Ref	Expression
sylanr1	|- ((ph /\ (ta /\ ch)) -> th)

Proof of Theorem sylanr1

Step	Hyp	Ref	Expression
1		sylanr1.1	. 2 |- ((ph /\ (ps /\ ch)) -> th)
2		sylanr1.2	. . 3 |- (ta -> ps)
3	2	anim1i 334	. 2 |- ((ta /\ ch) -> (ps /\ ch))
4	1, 3	sylan2 451	1 |- ((ph /\ (ta /\ ch)) -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  sbthlem9 4444  climge0 7065  lmsslem 7914  bcthlem21 7981  irredlem1 10273  irredlem3 10275

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