Theorem syl3an2b 862

Description: A syllogism inference.

Hypotheses

Ref	Expression
syl3an.1	|- ((ph /\ ps /\ ch) -> th)
syl3an2b.2	|- (ta <-> ps)

Assertion

Ref	Expression
syl3an2b	|- ((ph /\ ta /\ ch) -> th)

Proof of Theorem syl3an2b

Step	Hyp	Ref	Expression
1		syl3an.1	. 2 |- ((ph /\ ps /\ ch) -> th)
2		syl3an2b.2	. . 3 |- (ta <-> ps)
3	2	biimp 151	. 2 |- (ta -> ps)
4	1, 3	syl3an2 859	1 |- ((ph /\ ta /\ ch) -> th)

Syntax hints:   -> wi 3   <-> wb 146   /\ w3a 774

This theorem is referenced by:  omlimcl 4206  isum1p 7177  elcls3 7690

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  df-3an 776

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