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Mirrors > Home > NFE Home > Th. List > pm5.42 | GIF version |
Description: Theorem *5.42 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm5.42 | ⊢ ((φ → (ψ → χ)) ↔ (φ → (ψ → (φ ∧ χ)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ibar 490 | . . 3 ⊢ (φ → (χ ↔ (φ ∧ χ))) | |
2 | 1 | imbi2d 307 | . 2 ⊢ (φ → ((ψ → χ) ↔ (ψ → (φ ∧ χ)))) |
3 | 2 | pm5.74i 236 | 1 ⊢ ((φ → (ψ → χ)) ↔ (φ → (ψ → (φ ∧ χ)))) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ 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: anc2l 538 imdistan 670 |
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