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Mirrors > Home > ILE Home > Th. List > expcomd | GIF version |
Description: Deduction form of expcom 109. (Contributed by Alan Sare, 22-Jul-2012.) |
Ref | Expression |
---|---|
expcomd.1 | ⊢ (φ → ((ψ ∧ χ) → θ)) |
Ref | Expression |
---|---|
expcomd | ⊢ (φ → (χ → (ψ → θ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | expcomd.1 | . . 3 ⊢ (φ → ((ψ ∧ χ) → θ)) | |
2 | 1 | expd 245 | . 2 ⊢ (φ → (ψ → (χ → θ))) |
3 | 2 | com23 72 | 1 ⊢ (φ → (χ → (ψ → θ))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 101 |
This theorem is referenced by: simplbi2comg 1329 2moswapdc 1987 indifdir 3187 reupick 3215 trintssm 3861 issod 4047 poxp 5794 smores2 5850 smoiun 5857 recexprlemm 6596 ltleletr 6897 fzind 8129 iccid 8564 ssfzo12bi 8851 |
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