Theorem triantru3 34000

Description: A wff is equivalent to its conjunctions with truths. (Contributed by Peter Mazsa, 30-Nov-2018.)

Hypotheses

Ref	Expression
triantru3.1	|- ph
triantru3.2	|- ps

Assertion

Ref	Expression
triantru3	|- ( ch <-> ( ph /\ ps /\ ch ) )

Proof of Theorem triantru3

Step	Hyp	Ref	Expression
1		triantru3.1	. . 3 |- ph
2	1	biantrur 527	. 2 |- ( ( ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
3		triantru3.2	. . 3 |- ps
4	3	biantrur 527	. 2 |- ( ch <-> ( ps /\ ch ) )
5		3anass 1042	. 2 |- ( ( ph /\ ps /\ ch ) <-> ( ph /\ ( ps /\ ch ) ) )
6	2, 4, 5	3bitr4i 292	1 |- ( ch <-> ( ph /\ ps /\ ch ) )

Syntax hints:   <-> wb 196   /\ wa 384   /\ w3a 1037

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386  df-3an 1039

This theorem is referenced by: (None)