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  563  imimorbdc  908  sbcom2v  2045  mor  2129  r19.21t  2625  reu8  3022  ra5  3141  unissb  3963  reusv3  4604  zfregfr  4719  tfi  4727  fun11  5446  prime  9727  raluz2  9961  isprm3  12877  isprm4  12878  bj-inf2vnlem2  16914