Theorem ancri 535

Description: Deduction conjoining antecedent to right of consequent. (Contributed by NM, 15-Aug-1994.)

Hypothesis

Ref	Expression
ancri.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ancri	⊢ (φ → (ψ ∧ φ))

Proof of Theorem ancri

Step	Hyp	Ref	Expression
1		ancri.1	. 2 ⊢ (φ → ψ)
2		id 19	. 2 ⊢ (φ → φ)
3	1, 2	jca 518	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:  truan  1331  bamalip  2324  gencbvex  2902  funmo  5126  fo00  5319  eqfnov2  5591  caovmo  5646