Theorem bi2.04 248

Description: Logical equivalence of commuted antecedents. Part of Theorem *4.87 of [WhiteheadRussell] p. 122. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
bi2.04	|- ( ( ph -> ( ps -> ch ) ) <-> ( ps -> ( ph -> ch ) ) )

Proof of Theorem bi2.04

Step	Hyp	Ref	Expression
1		pm2.04 82	. 2 |- ( ( ph -> ( ps -> ch ) ) -> ( ps -> ( ph -> ch ) ) )
2		pm2.04 82	. 2 |- ( ( ps -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
3	1, 2	impbii 126	1 |- ( ( ph -> ( ps -> ch ) ) <-> ( ps -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 105

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  imim21b  253  pm4.87  557  imimorbdc  896  sbcom2v  1985  mor  2068  r19.21t  2552  reu8  2934  ra5  3052  unissb  3840  reusv3  4461  zfregfr  4574  tfi  4582  fun11  5284  prime  9352  raluz2  9579  isprm3  12118  isprm4  12119  bj-inf2vnlem2  14726