Theorem sylan12 355

Description: A syllogism inference.

Hypotheses

Ref	Expression
sylan12.1	|- (((ph /\ ps) /\ ch) -> th)
sylan12.2	|- (ta -> ps)

Assertion

Ref	Expression
sylan12	|- (((ph /\ ta ) /\ ch) -> th)

Proof of Theorem sylan12

Step	Hyp	Ref	Expression
1		sylan12.1	. 2 |- (((ph /\ ps) /\ ch) -> th)
2		sylan12.2	. . 3 |- (ta -> ps)
3	2	anim2i 270	. 2 |- ((ph /\ ta ) -> (ph /\ ps))
4	1, 3	sylan 343	1 |- (((ph /\ ta ) /\ ch) -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  fvco3 2867  oesuc 3134  oelim 3137  divadddivt 4264  infxpidmlem12 4944

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

This theorem depends on definitions:  df-bi 128  df-an 198

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