Theorem biimt 549

Description: A wff is equivalent to itself with true antecedent.

Assertion

Ref	Expression
biimt	|- (ph -> (ps <-> (ph -> ps)))

Proof of Theorem biimt

Step	Hyp	Ref	Expression
1		ax-1 3	. . 3 |- (ps -> (ph -> ps))
2	1	a1i 7	. 2 |- (ph -> (ps -> (ph -> ps)))
3		pm2.27 30	. 2 |- (ph -> ((ph -> ps) -> ps))
4	2, 3	impbid 397	1 |- (ph -> (ps <-> (ph -> ps)))

Syntax hints:   -> wi 2   <-> wb 127

This theorem is referenced by:  biorf 551  sbc5g 1450  sbc6g 1451  elrabsf 1456  r19.3rzv 1767  ralidm 1774  brecop 3242  kmlem12 3591  kmlem13 3592

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org