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Metamath Proof Explorer

Theorem jcad

Description: Deduction conjoining the consequents of two implications. Deduction form of jca and double deduction form of pm3.2 and pm3.2i . (Contributed by NM, 15-Jul-1993) (Proof shortened by Wolf Lammen, 23-Jul-2013)

	Ref	Expression
Hypotheses	jcad.1	$⊢ φ \to (ψ \to χ)$
	jcad.2	$⊢ φ \to (ψ \to θ)$
Assertion	jcad	$⊢ φ \to (ψ \to (χ \land θ))$

Proof

Step	Hyp	Ref	Expression
1		jcad.1	$⊢ φ \to (ψ \to χ)$
2		jcad.2	$⊢ φ \to (ψ \to θ)$
3		pm3.2	$⊢ χ \to (θ \to (χ \land θ))$
4	1 2 3	syl6c	$⊢ φ \to (ψ \to (χ \land θ))$