anim2d - New Foundations Explorer

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Theorem anim2d 548

Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 5-Aug-1993.)

**Hypothesis**
Ref	Expression
anim1d.1	⊢ (φ → (ψ → χ))

**Assertion**
Ref	Expression
anim2d	⊢ (φ → ((θ ∧ ψ) → (θ ∧ χ)))

**Proof of Theorem anim2d**
Step	Hyp	Ref	Expression
1		idd 21	. 2 ⊢ (φ → (θ → θ))
2		anim1d.1	. 2 ⊢ (φ → (ψ → χ))
3	1, 2	anim12d 546	1 ⊢ (φ → ((θ ∧ ψ) → (θ ∧ 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: moeq3 3013 ssel 3267 sscon 3400 uniss 3912 copsexg 4607 ssopab2 4712 coss1 4872 fununi 5160 imadif 5171 fss 5230 weds 5938