Theorem bnj240

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj240.1	⊢ ( 𝜓 → 𝜓′ )
	bnj240.2	⊢ ( 𝜒 → 𝜒′ )
Assertion	bnj240	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜓′ ∧ 𝜒′ ) )

Proof

Step	Hyp	Ref	Expression
1		bnj240.1	⊢ ( 𝜓 → 𝜓′ )
2		bnj240.2	⊢ ( 𝜒 → 𝜒′ )
3	1	3ad2ant1	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) → 𝜓′ )
4	2	3ad2ant2	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) → 𝜒′ )
5	3 4	jca	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) → ( 𝜓′ ∧ 𝜒′ ) )
6	5	3comr	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → ( 𝜓′ ∧ 𝜒′ ) )