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Mirrors > Home > ILE Home > Th. List > pm1.4 | GIF version |
Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 15-Nov-2012.) |
Ref | Expression |
---|---|
pm1.4 | ⊢ ((φ ∨ ψ) → (ψ ∨ φ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 631 | . 2 ⊢ (φ → (ψ ∨ φ)) | |
2 | orc 632 | . 2 ⊢ (ψ → (ψ ∨ φ)) | |
3 | 1, 2 | jaoi 635 | 1 ⊢ ((φ ∨ ψ) → (ψ ∨ φ)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∨ wo 628 |
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-io 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: orcom 646 orcoms 648 pm2.3 691 pm2.36 716 pm2.37 717 pm2.8 722 dveeq2or 1694 prneimg 3536 |
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