Theorem ancld 246

Description: Deduction conjoining antecedent to left of consequent in nested implication.

Hypothesis

Ref	Expression
ancld.1	⊢ (φ → (ψ → χ))

Assertion

Ref	Expression
ancld	⊢ (φ → (ψ → (ψ ∧ χ)))

Proof of Theorem ancld

Step	Hyp	Ref	Expression
1		ancld.1	. 2 ⊢ (φ → (ψ → χ))
2		ancl 242	. 2 ⊢ ((ψ → χ) → (ψ → (ψ ∧ χ)))
3	1, 2	syl 12	1 ⊢ (φ → (ψ → (ψ ∧ χ)))

Syntax hints:   → wi 2   ∧ wa 196

This theorem is referenced by:  mopick2 1057  cgsex2g 1368  cgsex4g 1369  preq12b 1874  dmcosseq 2572  relssres 2596  cores 2659  tz7.49 2997  suppsr2 4017  replimt 4798  pjthlem12 5236

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