Theorem bi2.04 247

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 125	1 |- ( ( ph -> ( ps -> ch ) ) <-> ( ps -> ( ph -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  imim21b  251  pm4.87  547  imimorbdc  882  sbcom2v  1965  mor  2048  r19.21t  2532  reu8  2908  ra5  3025  unissb  3803  reusv3  4421  zfregfr  4534  tfi  4542  fun11  5238  prime  9264  raluz2  9491  isprm3  11999  isprm4  12000  bj-inf2vnlem2  13588