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Mirrors > Home > ILE Home > Th. List > ord | Structured version GIF version |
Description: Deduce implication from disjunction. (Contributed by NM, 18-May-1994.) (Revised by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ord.1 | ⊢ (φ → (ψ ∨ χ)) |
Ref | Expression |
---|---|
ord | ⊢ (φ → (¬ ψ → χ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ord.1 | . 2 ⊢ (φ → (ψ ∨ χ)) | |
2 | pm2.53 628 | . 2 ⊢ ((ψ ∨ χ) → (¬ ψ → χ)) | |
3 | 1, 2 | syl 14 | 1 ⊢ (φ → (¬ ψ → χ)) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 616 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in2 533 ax-io 617 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: pm2.8 710 orcanai 825 ax-12 1384 swopo 4016 suc11g 4217 ordsoexmid 4222 nnsuc 4263 sotri2 4647 nnsucsssuc 5981 nntri2 5983 nntri1 5984 elni2 6167 nlt1pig 6193 bj-peano4 6522 |
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