Theorem ancl 242

Description: Conjoin antecedent to left of consequent.

Assertion

Ref	Expression
ancl	⊢ ((φ → ψ) → (φ → (φ ∧ ψ)))

Proof of Theorem ancl

Step	Hyp	Ref	Expression
1		pm3.2 232	. 2 ⊢ (φ → (ψ → (φ ∧ ψ)))
2	1	a2i 8	1 ⊢ ((φ → ψ) → (φ → (φ ∧ ψ)))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  ancld 246  anclb 264  pm4.71 481  exintr 793

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