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Mirrors > Home > NFE Home > Th. List > anim2d | GIF version |
Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
anim1d.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
anim2d | ⊢ (φ → ((θ ∧ ψ) → (θ ∧ χ))) |
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-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: moeq3 3013 ssel 3267 sscon 3400 uniss 3912 copsexg 4607 ssopab2 4712 coss1 4872 fununi 5160 imadif 5171 fss 5230 weds 5938 |
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