Theorem biantrud 493

Description: A wff is equivalent to its conjunction with truth. (Contributed by NM, 2-Aug-1994.) (Proof shortened by Wolf Lammen, 23-Oct-2013.)

Hypothesis

Ref	Expression
biantrud.1	|- (ph -> ps)

Assertion

Ref	Expression
biantrud	|- (ph -> (ch <-> (ch /\ ps)))

Proof of Theorem biantrud

Step	Hyp	Ref	Expression
1		biantrud.1	. 2 |- (ph -> ps)
2		iba 489	. 2 |- (ps -> (ch <-> (ch /\ ps)))
3	1, 2	syl 15	1 |- (ph -> (ch <-> (ch /\ ps)))

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by:  ssofss  4077  eqtfinrelk  4487  ovmpt2x  5713  clos1induct  5881