Theorem 2thd 231

Description: Two truths are equivalent (deduction rule). (Contributed by NM, 3-Jun-2012.)

Hypotheses

Ref	Expression
2thd.1	⊢ (φ → ψ)
2thd.2	⊢ (φ → χ)

Assertion

Ref	Expression
2thd	⊢ (φ → (ψ ↔ χ))

Proof of Theorem 2thd

Step	Hyp	Ref	Expression
1		2thd.1	. 2 ⊢ (φ → ψ)
2		2thd.2	. 2 ⊢ (φ → χ)
3		pm5.1im 229	. 2 ⊢ (ψ → (χ → (ψ ↔ χ)))
4	1, 2, 3	sylc 56	1 ⊢ (φ → (ψ ↔ χ))

Syntax hints:   → wi 4   ↔ wb 176

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 177

This theorem is referenced by:  had1  1402  sbc2or  3055  abvor0  3568  ralidm  3654  fcnvres  5244