Theorem 2th 540

Description: Two truths are equivalent.

Hypotheses

Ref	Expression
2th.1	⊢ φ
2th.2	⊢ ψ

Assertion

Ref	Expression
2th	⊢ (φ ↔ ψ)

Proof of Theorem 2th

Step	Hyp	Ref	Expression
1		2th.2	. . 3 ⊢ ψ
2	1	a1i 7	. 2 ⊢ (φ → ψ)
3		2th.1	. . 3 ⊢ φ
4	3	a1i 7	. 2 ⊢ (ψ → φ)
5	2, 4	impbi 139	1 ⊢ (φ ↔ ψ)

Syntax hints:   ↔ wb 127

This theorem is referenced by:  dfnul2 1709  dfnul3 1710  pwv 1884  int0 1978  orduninsuc 2365  dmi 2545  fo1st 3094  fo2nd 3095  1st2val 3097  jech9.3 3510  nn0ltp1let 4556

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

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