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Mirrors > Home > ILE Home > Th. List > ax-ia3 | GIF version |
Description: 'And' introduction. Axiom 3 of 10 for intuitionistic logic. (Contributed by Mario Carneiro, 31-Jan-2015.) |
Ref | Expression |
---|---|
ax-ia3 | ⊢ (φ → (ψ → (φ ∧ ψ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wph | . 2 wff φ | |
2 | wps | . . 3 wff ψ | |
3 | 1, 2 | wa 97 | . . 3 wff (φ ∧ ψ) |
4 | 2, 3 | wi 4 | . 2 wff (ψ → (φ ∧ ψ)) |
5 | 1, 4 | wi 4 | 1 wff (φ → (ψ → (φ ∧ ψ))) |
Colors of variables: wff set class |
This axiom is referenced by: ex 108 pm3.2 126 pm5.54dc 826 pclem6 1264 xoranor 1267 ax10oe 1675 2pwuninelg 5839 dmaddpq 6363 dmmulpq 6364 ltsopr 6570 ax1hfs 9233 |
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