Theorem jctl 525

Description: Inference conjoining a theorem to the left of a consequent. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 24-Oct-2012.)

Hypothesis

Ref	Expression
jctl.1	⊢ ψ

Assertion

Ref	Expression
jctl	⊢ (φ → (ψ ∧ φ))

Proof of Theorem jctl

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2		jctl.1	. 2 ⊢ ψ
3	1, 2	jctil 523	1 ⊢ (φ → (ψ ∧ φ))

Syntax hints:   → wi 4   ∧ wa 358

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  df-an 360

This theorem is referenced by:  mpanl1  661  mpanlr1  667  nchoicelem5  6294