Theorem ancli 534

Description: Deduction conjoining antecedent to left of consequent. (Contributed by NM, 12-Aug-1993.)

Hypothesis

Ref	Expression
ancli.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ancli	⊢ (φ → (φ ∧ ψ))

Proof of Theorem ancli

Step	Hyp	Ref	Expression
1		id 19	. 2 ⊢ (φ → φ)
2		ancli.1	. 2 ⊢ (φ → ψ)
3	1, 2	jca 518	1 ⊢ (φ → (φ ∧ ψ))

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:  pm4.45im  545  mo  2226  2mo  2282  barbari  2305  cesaro  2311  camestros  2312  calemos  2322  lecidg  6196  addlec  6208