Theorem jctl 238

Description: Inference conjoining a theorem to the left of a consequent.

Hypothesis

Ref	Expression
jctl.1	⊢ ψ

Assertion

Ref	Expression
jctl	⊢ (φ → (ψ ∧ φ))

Proof of Theorem jctl

Step	Hyp	Ref	Expression
1		jctl.1	. . 3 ⊢ ψ
2	1	a1i 7	. 2 ⊢ (φ → ψ)
3		id 9	. 2 ⊢ (φ → φ)
4	2, 3	jca 236	1 ⊢ (φ → (ψ ∧ φ))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  eqvin.l1 851  rabab 1359  vss 1729  recdivt 4270  pjpj0 5259  ococint 5298  shunss 5338  cmbr4 5510

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

metamath.org