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Mirrors > Home > MPE Home > Th. List > pm1.4 | Structured version Visualization version GIF version |
Description: Axiom *1.4 of [WhiteheadRussell] p. 96. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm1.4 | ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | olc 866 | . 2 ⊢ (𝜑 → (𝜓 ∨ 𝜑)) | |
2 | orc 865 | . 2 ⊢ (𝜓 → (𝜓 ∨ 𝜑)) | |
3 | 1, 2 | jaoi 855 | 1 ⊢ ((𝜑 ∨ 𝜓) → (𝜓 ∨ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∨ wo 845 |
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 206 df-or 846 |
This theorem is referenced by: orcom 868 orcoms 870 pm2.3 922 pm2.36 967 pm2.37 968 rb-ax2 1748 prneimg 4861 cnf2dd 37792 orcomdd 37868 rp-fakeanorass 43180 orbi1rVD 44524 itsclc0yqsol 48152 |
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