Theorem bitr2d 178

Description: Deduction form of bitr2i 174. (Contributed by NM, 9-Jun-2004.)

Hypotheses

Ref	Expression
bitr2d.1	|- (ph -> (ps <-> ch))
bitr2d.2	|- (ph -> (ch <-> th))

Assertion

Ref	Expression
bitr2d	|- (ph -> (th <-> ps))

Proof of Theorem bitr2d

Step	Hyp	Ref	Expression
1		bitr2d.1	. . 3 |- (ph -> (ps <-> ch))
2		bitr2d.2	. . 3 |- (ph -> (ch <-> th))
3	1, 2	bitrd 177	. 2 |- (ph -> (ps <-> th))
4	3	bicomd 129	1 |- (ph -> (th <-> ps))

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  3bitrrd  204  3bitr2rd  206  pm5.18dc  776  drex1  1676  elrnmpt1  4528  xpopth  5744  sbcopeq1a  5755  ltnnnq  6406  ltaddsub  7226  leaddsub  7228  posdif  7245  lesub1  7246  ltsub1  7248  lesub0  7269  ltdivmul  7623  ledivmul  7624  zlem1lt  8076  zltlem1  8077  fzrev2  8717  fz1sbc  8728  elfzp1b  8729  sumsqeq0  8985