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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 1332 2moswapdc 1990 indifdir 3193 reupick 3221 trintssm 3870 issod 4056 poxp 5853 smores2 5909 smoiun 5916 recexprlemm 6722 ltleletr 7100 fzind 8353 iccid 8794 ssfzo12bi 9081 |
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