Theorem simplbi2com

Description: A deduction eliminating a conjunct, similar to simplbi2 . (Contributed by Alan Sare, 22-Jul-2012) (Proof shortened by Wolf Lammen, 10-Nov-2012)

	Ref	Expression
Hypothesis	simplbi2com.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
Assertion	simplbi2com	⊢ ( 𝜒 → ( 𝜓 → 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		simplbi2com.1	⊢ ( 𝜑 ↔ ( 𝜓 ∧ 𝜒 ) )
2	1	simplbi2	⊢ ( 𝜓 → ( 𝜒 → 𝜑 ) )
3	2	com12	⊢ ( 𝜒 → ( 𝜓 → 𝜑 ) )