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Theorem ancld 536

Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.)

**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		idd 21	. 2 ⊢ (φ → (ψ → ψ))
2		ancld.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	jcad 519	1 ⊢ (φ → (ψ → (ψ ∧ χ)))

Colors of variables: wff setvar class

Syntax hints: → wi 4 ∧ wa 358

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8

This theorem depends on definitions: df-bi 177 df-an 360

This theorem is referenced by: mopick2 2271 cgsexg 2890 cgsex2g 2891 cgsex4g 2892 reximdva0 3561 difsn 3845 preq12b 4127 nnpw1ex 4484 tfin11 4493 vinf 4555 dmcosseq 4973 ssreseq 4997 fnoprabg 5585 dmfrec 6316

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