Theorem sylan2br 462

Description: A syllogism inference. (Contributed by NM, 21-Apr-1994.)

Hypotheses

Ref	Expression
sylan2br.1	|- (ch <-> ph)
sylan2br.2	|- ((ps /\ ch) -> th)

Assertion

Ref	Expression
sylan2br	|- ((ps /\ ph) -> th)

Proof of Theorem sylan2br

Step	Hyp	Ref	Expression
1		sylan2br.1	. . 3 |- (ch <-> ph)
2	1	biimpri 197	. 2 |- (ph -> ch)
3		sylan2br.2	. 2 |- ((ps /\ ch) -> th)
4	2, 3	sylan2 460	1 |- ((ps /\ ph) -> th)

Syntax hints:   -> wi 4   <-> wb 176   /\ wa 358

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  df-an 360

This theorem is referenced by:  syl2anbr  466  imainss  5043  xpexr2  5111  funeu2  5133  imadif  5172  fnop  5187  fcnvres  5244  fnopovb  5558  fovrn  5605  fnovrn  5608  nchoicelem17  6306